This type of symptom can be lots of things but is most classically, carbs or fuel delivery.
Check compression, yes. Check temp sensors & warning horn - good idea too, as is installing a temperature gauge so you got a clue before it's already too hot (although testing temp sensors requires removing water jackets on heads, which is usually easy but can be tricky if a bolt is stuck).
Sanity check link and sync for anything goofy, yes - ie carb butterflies run together and are closed at idle, trigger assembly turns as expected with throttle before carbs start opening, everything all connected together.
A new-to-you engine, you replace water pump and any thermostats/poppet-valves AND it's a good idea to service both the fuel pump (what is applicable), any hoses that look questionable, replace any filters involved, and rebuild the carbs. Removing the heads, checking the water deflectors, removing the covers, cleaning out the jackets on the heads, putting it all together nice and clean with new gaskets, is also great to do, however it can get you in trouble if bolts are stuck (usually aren't but can be).
Bad fuel usually shows up as a problem starting an engine. Something that runs well at idle, likely has good fuel. But that doesn't mean you don't have a filter that is plugged up due to bad fuel and is restricting flow.
Bogging, stalling, when you try to go wide open, is usually clogged up carburetor/jets - it's a common every 5 years sort of job, you get the kits, remove, disassemble, clean, rebuild, and put the carbs back on. Usually even if you didn't note anything wrong the problem is corrected.
If this engine is using a non VRO fuel pump, ie the style that the 88 SPL has, the style from back prior to VRO's that mounts to the block, when the diaphragms go they tend to come apart and clog the carbs. It's a good practice to replace the fuel pump, or put a rebuild kit in what you got, each time you do the carbs for this reason - new fuel pump components will outlast your carb rebuild but do not last forever.