Sounds like a fuel issue of some sort. If it's losing power wide-open (I'm assuming while cutting?), that sounds like it's running lean on the High jet. You didn't mention if it's holding an idle properly and throttling up smoothly, but if it is, then that should more or less rule out an air leak in the fuel lines or crank seals. When you say the fuel line is "open", do you mean that you can blow on the intake line and blow right through the carb? Because this should be impossible unless you're also pressing on the diaphragm to open the valve inside the carb. If this is the case, then the saw is getting WAY too much gas, but I can't believe you'd even get it to start under this condition. If it's any help, the way I tune most carbs is as follows:
-turn both jet screws out about 1 turn
-start the saw, and tune the High jet to where it sounds proper (unless you have a tach)
-tune the Low jet so that the engine accelerates smoothly to top throttle
-turn the Idle adjustment screw so that the engine holds a smooth idle without the chain jumping forward
I don't know if you've checked
THIS PAGE out, it has pretty much all the stats for that saw. It says your spark plug should be a Champion CJ-6 or equivalent - check that yours is right, because the wrong one can cause all sorts of weird problems. If your coil was bad, the saw would likely run really rough or quit altogether, and/or be hard to re-start, after it gets hot.
The only other possibilities I can think of are corroded or bent reed valves, or maybe the aftermarket piston is clearing the ports differently or something. Unless that saw has a governor, my 090 will not hit top RPM when out of the cut due to the governor, but it doesn't affect the RPMs and power when cutting.