I agree on the shock treatment. Hopefully, you have a 3 gallon tank. Drain your vapor separator before you begin the process, so you do not have to burn through the gas before you actually "treat" the engine.
It sounds like you know what you are doing if you replaced the pistons and rings. Since that was an unknown before....have you double checked to be sure that the timing marks are still lined up. If the chain is off just one notch, it can cause all kinds of unusual things.
Normally, the chain will not jump time unless the tensioner had an issue or if the cam chain guides deteriorate.
For others reading this....the chain, tensioner, etc are totally enclosed and bathed in oil....so it is very unlikely that a critter built a nest...as happens a lot with engines with exposed timing "belts".
Back to your decarb....
The way I do it...since we do not have direct access to water (it is just up the street, though)....After draining the vapor separator, I run the engine on the decarb tank for about 20 minutes at a fast idle, on a hose. Then I let it sit for an hour or so. After sitting, I run the engine a little faster for the first few minutes, then, I repeat the process about three more times. If I have originally found a problem with the compression, I repeat the compression test on the problem cylinder or two about 1/2 way through the process to see if it is doing any good.
Once I do that process, I take it to the water and back it in and run up the rpms in gear, on the trailer, up to mid range. I want to be sure it gets well up to temperature to burn the crap out.
Finally, one more compression test...sometimes even a leakdown test....again...depending on what problem I was trying to fix.
All that being said....if you have access to water, all the steps would be better in the water under load. Of course, you have to sit and wait for an hour or two or more between steps to let the solution do its work.
Be sure to change the oil after all is finished.
I would change the spark plugs, but in your case, you may be able to put them in some solution to clean them up. You certainly should not use a mechanical cleaning process or you may ruin the plugs for sure.
Mike