My son's 86 MR2 got a cylinder head shaved and is stalling now

Assuming that the timing chain is in the correct position, and you do not have compression in any of the cylinders, you will need to check if any of the valved are bent by taking off the rockers and inserting air into the spark plug holes and see where the air goes. Either through the intake or the exhaust. If the air is escaping, then the pistons probably have hit the valves while they were open.

Are you saying you are getting water in the top cylinder even after doing Head gaskets? How clean was the Engine Block where the gasket sits? sure sounds like you still have a coolant leak to the cylinder

if it is just one and the mechanic is reasonable and there is no other damage ,ie main bearings, valves, cylinders scored, around 800 per head gasket and if one head needs to be shaved you better get the other head shaved and gasket replaced..i had my 2000 taurus done for 1200 couple years ago. it ran for a few years then developed low compression from the coolant leaking into the cylinders..never had luck with mine hope you are having better luck

Have you done a wet compression test on all the cylinders, which entails squirting some oil (about 1/4 cup) into the plug holes to help seal around the rings and re-doing the compession test.
If the pressure goes up by a fair amount (40 - 60 Lbs) then it is definitely the rings but if it only increases by around 20 lbs then it is either valves or the head gasket is leaking between #2 & # 3.
I would first suspest a warped head , especially if engine hsa been run low on coolant and allowed to over heat.
Removal of the head can be done with engine in place. Once off, check the face of the head with a straight edge and if not true have it machined by an engine reconditioner. While the head is off, it may be advisable to check the valves and valve seats for wear and replace the valve stem seals as they tend to be worn and and hard due the age of the vehicle. If the engine is fitted wth a timing belt it may be advisable to replace this also if more than 50,000 miles / 80,00 Km has elapsed since it was last changed.

coil or electronic ignition module going off when turning warmer.i guess run some test

Check all the wiring connections that you loosened or took off when you removed the head. something is loose or disconnected ,eg., ground wires .
Make sure you have spark at spark plugs whemn cranking ,and fuel pressure.
Did you try spraying starting-fluid in the intake, see if the engine runs for a little bit.
Compression to be anything above 100 psi will firean engine ,sometimes lower too.

It is very likely the overheating has blown the cylinder head gasket and coolant is getting into cylinders or compression is leaking from cylinder to cylinder or both, you will need to remove the cylinder head and have it checked for warp-age and shaved flat by a machine shop if ness, and replace heat gasket.

Did you have the head machined/shaved before you replaced the head gasket with a new one? If not--do over---machine head---replace gasket.

BUT, before you even bother, have you considered the fact that the BLOCK may be cracked? You can check this by looking at each spark (plug for combustion residue of coolant or oil) of each cylinder separately.

the white smoke as it stalls could be steam in the exhaust. This is caused by coolant leaking into cylinders from a leaking head gasket. You should check cylinder compression next with a compression tester.

If you have a head gasket leaking, and your engine is blowing a white smoke from the exhaust pipe, then you're taking coolant/water into your piston/s.

After a heavy acceleration your pressure is forcing more coolant/water into your cylinders..but don't be fooled..water/coolant is also getting into your cylinder/s when you're driving slow too.

You should get the head gasket repaired as soon as you can, or the head gasket may very well let loose and then you get to deal with having the heads shaved if they warp from the heat.

Either way..you really should get the gasket replaced soon.