Intermittent misfire low RPM

I get intermittent violent shaking on a light acceleration around 15-20 mph.
Mostly on a hot engine. If I accelerate moderate to hard the shaking instantly stops.
Random misfire codes get set but it is usually 1 or 2. No other codes.
It happens more the hotter it is out. At 85 deg it happens a lot. I drove it 15 miles today at 64 degrees out with about 30 stops and starts and it only happened once for what felt like 3 misfires.

Gen 3 2010 car has 220,000 miles 5k miles per qt of oil, runs quiet.
Here is what has been done
The spark plugs and coil packs have only around 30K
I changed all injectors
no difference
Then the real fun started
I removed the EGR cooler (was plugged solid), valve and pipe and cleaned them all.
same problem.
I replaced the EGR valve and removed the intake manifold and cleaned it (no passages were blocked).
Replaced the PCV valve.
Same problem
Just because it was cheap and easy, I replaced the cam advance solenoid thinking it might have an intermittent coil. no difference
Since all the engine parts should be the same temperature when the engine is hot regardless of the ambient temperature. I am starting to suspect the ECU computer. No 85 deg days currently in the forecast when I get one I'll pack the ECU in ice packs and test drive it.

Any other suggestions are appreciated?
Thanks in advance.

 

Thanks for the input. looks like the head gasket. I did a very simple test. I removed the coolant pressure cap. No pressure on the coolant no misfires, and I believe I have been losing a small amount of coolant.
Can anyone give me an Idea on how long it takes to replace the head gasket DYI?
By chance does anyone know of someone in the buffalo NY area that might do this economically.

 

Update 8-6-21
So I had the head gasket replaced all is good now.
I changed the water pump also just because it also had 218,400 miles
Here is list of the parts and labor cost just for everyone's reading pleasure.

$700 labor + $20 misc parts done as a side job
7/18/2021 218400 Head gasket kits & Head Bolts - rock auto $165
7/18/2021 218400 Timing Chain Kit Amazon $109
7/18/2021 218400 Coolant Toyota Pink Amazon $50
7/18/2021 218400 Water Pump Aisin Amazon $216
7/18/2021 218400 Oil And Filter $35
Total Head gasket $1290

Mechanic said it is the cleanest engine he has ever seen with 200K miles. Car has 218K miles.
Mostly used Mobil1 full synthetic, and used some Pennzoil full synthetic. 10K mile change interval.
I actually believe this problem started about 2 years ago, and that's what drove me to change the spark plugs and coil packs.
I changed the water pump just because it was still the original. Aisin is the OEM manufacturer.
I just treated it to a new set of front brakes, 70K miles on them. they likely would have passed NYS inspection but were close.
I'll likely replace the inverter coolant pump and change the transmission oil in the near future.
Good for another 100,000 miles !