Yes, I did change to a set of colder plugs when I did the mods, to account for the extra boost and such. I'm going to rule out my plugs for now, as I really don't think changing them to a step EVEN colder will do the car any good. You're correct though, the hot tip may be the culprit however it makes the same sound when I put in stock plugs with that strange design that are the stock heat rating. 

I did try an octane booster previously, but they're cheap so I'll give it another shot. I'm also going to try a de-carbon treatment by means of spraying something (I don't want to pull the head if I don't have to )

did you ever change to colder plugs?
You had mentioned that this would lower the combustion chamber temperature.
Much more likely, it would lower the spark plug temperature and if a hot plug was the cause of preignition then that might help.

Kaelan, some "maybes":

Maybe the car was doing it before you got it (as you suspect).
Maybe the previous owner didn't drive it hard enough to keep the engine cleaned out.
Maybe the carbon buildup is to the point of increasing the compression ratio.
Maybe the previous owner was advised the engine needed the head removed and the combustion chambers cleaned and decided not to spent that much.

or Maybe not!

Let me jot down my thoughts about detonation:

Detonation (or engine knock) means the combustion is happening before the piston reaches top dead center. Typical causes are lean air/fuel mix, timing too far advanced, compression too high, combustion temps too high.

'Normally', the computer would detect detonation from the knock sensor and pull back the timing and richen the air/fuel mix. This should stop the detonation.

Some high performance engines require high octane fuel to keep it from detonation. Perhaps you might try adding an octane boost additive to see if the noise changes?

We've mentioned carbon deposits on the pistons because the buildup takes up volume which in turn increases the compression ratio.

Air/fuel can run lean with a leak in the intake system, where more air is added to the metered fuel thus creating a lean condition.

Clogged fuel injectors may have trouble delivering enough fuel to keep the mixture correct.

Perhaps all this has been already discussed, but maybe someone else can add to the discussion.

I'll do some digging and find some good products. But when I cleaned the valves it was more to clean the manifold out, as I pulled it off along with the rest of the piping on the intake side and cleaned it out thoroughly. I sprayed some specialized intake manifold and throttle body cleaner and gave it a good scrub, and I thought I might as well spray some around the valves (when seated) and let it sit for a while to see if anything leaked through the valve seat and to give it a good clean. I found none of my intake valves let a noticeable amount of cleaner through so I put everything back on with some new gaskets and that was that. I thought that cleaning the whole intake side of the engine out might help with the "crackling" but this was one of my early attempts at fixing it about 6 months ago. Thanks for the suggestions

That's a pretty spot-on description unfortunately for me. It sounds like glass beads being dropping into the cylinder then they go away, and come back. It's really hard to describe but marbles are probably the best one. So it is detonation then. 

The only thing that really has me beat is why is it happening to this mini in particular? 

Purchased with low miles, good condition, well maintained, and now it comes to me (I do not like to unnecessarily push the car at every stop sign and red light) and has this bizarre issue. Maybe it always had this issue, but would you all agree that pretty much everyone who does a 15% pulley, ignition, and CAI doesn't see a similar issue? So it must be a mechanical part at fault or maybe a tuning issue? (has stock tune as far as I can tell)

However, I'm also quite positive that when I did the CAI and ignition prior to the pulley swap, it had the same issue. 

I really am getting stumped and any suggestions will be greatly appreciated. 

Sorry, I personally can't suggest a product as I haven't used one on many years, and it was on a classic Mini. As I am in Canada my suggestion would probably not be relevant to your location. With my Mini, it was a small matter of removing the air cleaner and spraying the treatment into the carb. You don't have a carb and do have a supercharger and an assortment of intake and exhaust sensors to consider.
Perhaps those familiar with new MINIs can make suggestions of a safe, appropriate product and how to use it.

I am surprised you could remove carbon from the intake valves on the manifold side - all you'd see would be the stem and back of the valve head, and I'd be surprised to see any significant carbon there because each valve would be closed tight at combustion. I suppose though, if you did/do have pre-ignition, there might have been blow-back through the valve, or the valves aren't sealing well.

The carbon in a cylinder that would cause pre-ignition would be a hard, ceramic like build-up, not a soft, wipe-able soot. Typically the treatment is used on a hot engine when the deposit is good and hot. When the chemical hits it, the deposit suddenly cools and cracks of and goes out the exhaust system. In the really old days, water would be dribbled into the carb carefully so as to NOT chill the valves and damage them. I have also seen transmission fluid used in the same way - supposedly much easier on the valves. (It makes a huge cloud of white smoke!) But I wouldn't use either on a modern engine.

The claim from Pennzoil is it's auto ignition caused by ash or micro oil droplets. Their theory is the detergent additive causes the problem, by changing the detergent mix it will prevent/reduce the chance of the LSPI. Bottom line I would just make sure on the next oil change to use API SN plus oil, probably costs no extra. This is just a small DI turbo engine problem.

Detonation in an engine to me 'sounds like' loose marbles in the engine. Does this sound like what you are hearing?

Just want to try to be sure before you spend more $$...

Not likely, I might have to look into purchasing one.

I looked it up, but can an oil really change the chance for pre-ignition or detonation? Unless it drops the temp down maybe?

I did a de-carbon on the intake valves by removing the intake manifold when I serviced the supercharger, but not in the cylinders. Can you recommend anything for this?

Thanks for the feedback.

can you get a hold of a borescope to inspect the tops of the pistons inside the cylinders  for carbon buildup?

API service SN plus and Dexos Gen2 motor oils are designed to prevent a new type of low speed pre-ignition found in DI turbo engines. Go figure.

If you have been experiencing irregular fueling due to the faulty knock sensor, your cylinders may have a carbon buildup. Carbon can heat up and cause pre-ignition. Try (if you can or haven't already) using a de-carbon treatment.

Hello once again, I had a great evaluation written out but chrome decided to stop working so here we are again. 

Bottom line, "crackling" sound upon heavy acceleration wouldn't go away with changes in my ignition system, or an octane booster, so it was ruled down to a faulty knock sensor. 

I replaced the sensor and it worked! But "worked" is a relative term. The crackling subsided to a significant extent, but there is still a crackle audible while under hard acceleration every now and then while doing a pull. 

I really am not satisfied with the fix yet because it still doesn't seem "fixed" to me. I read a forum on spark plugs, and I might try a copper or silver plug. I read that the Iridium ones I have don't lend a hand towards much of a performance gain and that they're for longevity. Being that my Mini is experiencing detonation, it means the combustion temperatures are too great, so a colder plug is needed to transfer more heat from the combustion process to the cylinder head itself, lowering the combustion temperature and reducing the chance for detonation. The only issue is that I already have a one-step colder set of plugs in my Mini right now, and I have almost since I originally purchased the car. I don't want to put two-step colder plugs in because I know I am not making the kind of power needed for a plug of that rating with the mods I have done (15% Sc pulley, CAI, MSD ignition) 

So it looks like I'm running out of options. I'm going to throw the old ignition and plugs in to see if it makes a difference with the new knock sensor, but other than that I really don't know what to do.

BTW- if you're thinking of changing your knock sensor, you can test the old one while it's still in the car with a multimeter, so you don't waste your time pulling everything apart to get to it. I read that a reading of 500-600 kiloOhms is a healthy sensor (on most vehicles). I'm not 100% on how applicable this info is to our Minis but I couldn't find much info on the surface. I didn't actually do this test yet, so I can get some numbers for a fallowup.

Thanks for the help

Let us know what you find out!

I'm doing an octane booster test to see if that makes any changes and if not, it's looking like the knock sensor is the only thing left to check.

Maybe a new knock sensor?