Ok guess I'll give some suggestions even though I not that familar with that model of honda, I have honda GX on generator maybe it the same? First I would see if I'm getting gas to the carb. by removing the gas line from the carb., primer bulb and seeing if gas is flowing down stream. Next I would verify I hooked up the hoses right that you replaced.

Now that I know I'm getting gas to the carb. Next I would suspect the float is stuck (if it has one)? you can try tapping on the carb. bowl, but I would just take the bowl back off and see if gas is running through the carb.from the gas tank.

When I mess with the float I alway attach rubber hose and blow through it to make sure I got flow, then I flip it up side down while still blowing through and see if the float cuts the air flow off. If so I know the float is working (may not be adjusted right but I alows flow and stops it).

Another thing about priming spoon full of gas is too much all that does is wet the plug and too much raw gas in the comb. chamber for it to lite off. this IMO is why you are having to crank so long to get it to fire. I use carb. cleaner and maybe two second blast down the carb. or spark plug hole. Carb. cleaner will evaporate alot quicker than gas and the engine should spool up some when it hits off it.

this should reveal something if not maybe some one else will respond?

Well I believe you have pretty well summed it up RC . However being a 4-Stroke Valve issues could play into the equation (Stuck Valve) if the air entrailment leaned out the engine for any extended duration . Even then the engine should at least sputter or attempt to fire ? I think the Fuel restriction as you have indicated may not be the key , puzzling since with carb cleaner sprayed within the carb or plug hole the engine should respond . Sounds like less than adequate compression , leaning back to valve sealing issues perhaps ?