Intermittent bogging under load tells me some kind of fuel starvation or a vacuum leak somewhere. If it works fine then bogs but can work fine sometimes it could very well be a carburetion issue or a kinked fuel line, it could also be a blown gasket between the head and intake or carb and intake, or if it has a plastic intake it could have a crack in it that can't be seen easily, but can drive someone nuts trying to figure out what's wrong. Have you tried spraying carb cleaner on the intake when it's bogging to see if things get better while the carb cleaner is being sprayed on the intake?
I'm thinking it's either air getting into the engine somewhere besides the carb or there's something keeping the fuel from getting into the carb, or something in the carb not letting the fuel get in or get out. Does the carb have a float? And does it move freely every time? Does the needle and seat valve have a little spring on the needle that may be keeping it closed when it should be open?
I would be checking out everything in the carb that handles fuel or air as well as well.
Another thing to look at is see if it's overheating, some of these smaller engines can be sensative to things like cooling shrouds or dusty/dirty cylinder fins, too much paint on the cylinder fins, etc... if it's missing any cooling shrouds or air deflectors... or any restriction anywhere where cooling air can get into or out of the cooling system.
Look at the head bolts and see if they're torqued down properly as they may be ok until the engine warms up then become very boggy if compression is lost or reduced either from too much heat causing a small warpage, or even a loose spark plug could cause the bogging, so can carbon buildup on the valves not allowing them to completely close, and in a worst case scenario, worn out rings or a scratched cylinder.
Anything that can cause a loss of compression can make the engine really boggy so if everything else looks good, it could be a loss of compression.