Thank you for your responses gents. Have definitely steered me in the right direction. 

Plan now is SW5 cam, twin 1 1/2, Maniflow RC40 and new Hypatec pistons.

I will get exhaust valve inserts and head serviced. Hopefully the above will give me a nice usable road motor.

The engine gurus should chime in shortly but until then...

Purely a guess here but the last guy who was in the motor might have found a weird piston like a Maxi piston or some such and bored to fit.  It ran ok because it was low on compression rather than super high compression.  If the flat tops were used in a 1360 and the block were decked like normal, the compression ratio would have been through the roof, assuming the chambers are within the "normal" range.  So, this person was solving a problem in a strange way buy hey, we weren't there to vote in the matter.
I would cc the chambers and invest some time figuring out what you have in regard to your cylinder head before you make your next move.  In the Yellow Bible, Vizard coaches us through the process of calculating compression ratio, which can be your friend of your enemy, depending 

A bit more reading on line and I am now assuming the block was bored to 73mm but had wrong pistons fitted. Makes sense of the 140psi compression before I pulled it down. Had never driven.

1360 with proper pistons fitted. Hypatec 73 are about 7 mm taller from wrist centre to top. That will bring the new piston very close to top of block. 

Fortunately the bored look pretty fresh so I’ll put the Hypatec, fit a Kent 266? And have unleaded inserts fitted. From what I understand I could go 1380 which I don’t but I need to make sure I can sleeve if I need to later. 

Have answered some of my own questions!

Any recommendations on head gasket?

Crankshaft AEG 460
Head 12G940
Rod AEG521
Rod cap AEG145
Piston A256 1X   STD
then TOP 0 03 WY
Block. 9FXEY55418

Offset from what I now understand is cylinder alignment. In my case all in line.

Thanks for info and questions!

Took some measurements this morning.

Stroke on my verniers 80.66 so no doubt standard.

Bore 73mm

Centre of wrist pin to centre of big end approx 146mm

Centre of wrist pin to piston top (flat top) is 32mm

Part number on Pistons A2561X ST   and.    OP O O3 W

Not sure how to check offset bore?

Crankshaft.  AEG 460. with EN40B also

Gap between cylinders. 2&3 is 3mm

1&4 are 3.9 to cylinders 2 and 3.

I will upload some photos off my phone shortly

thanks

Several questions come to mind
1 - what crankshaft is it ? standard stroke or 84 mm, 86 mm, or ? as was stated above a shortened piston for a stroked crank.
2 - are there any part numbers on the pistons ?
Graham Russel engineering comes to mind as they were producing a 73 mm piston for the Mini got to their web site and look at their pistons. as they sell a 73 mm piston.
3 - was the block offset bored when they went to 73 mm ?
What I'm asking here is how much is available between cylinders 2 - 3 to do an overbore ? - the reason they went to offset boring.
Going back to David Vizard's TBASE ( Tuning the British Leyland A Series Engine ) or in HTMYM ( How to Modify Your Mini ) he discusses "big bore" engines, the chances of hitting an oil line going to 73.5 or larger ( 74, 74.something - don't have the reference in front of me - but they were using a longer stroke producing a 1600 cc engine ), the don't use a Cooper 'S engine as they are rare and hard to find.

When I did my 1380 I used the "Mega Pistons" as sold by Mini Spares at the time - because Omega wasn't producing enough pistons to meet the need. I built a 1430 using them as well and a 1430 using Omega 73.5 mm pistons that were made for the stroked application.

Sounds more like you have short height 73mm pistons to match a stroked crank.

Which bits are going back in as-is and what are you changing ?

Thanks Doug 
i just measured the bore at 73mm. The pistons in it say STD. On web search 73mm is the 1370 overbore. Confusing. Obv the pistons are standard for some other motor. I was planning on reboring as very slight ovaling but no ridge. Sounds like73.5 1380 might be the last option other than resleave. 

I am not the person to put the pieces of this puzzle together but it sure sounds like at least one of the components is not "right" (crank, con rods, pistons).  I think you need to measure each to determine what combination is positioning the pistons 7.1mm below deck.

I am rebuilding my cooper s mk2 engine and it is std. bore. It looks as though the pistons were replaced with flat tops. Deck clearance is 7.1 mm with first compression ring 5mm down from piston top.
This seems way too big deck clearance. I assume the replacement AE pistons will be much closer to the deck? Is this just a rebuild stuff up by a incompetent mechanic?