Need a little small engine assitance, if possible...

And the trimmer head free wheels with the engine off/idling?, and the gearbox isn't blazing hot?

A)Running great when cold tells me she's not lean at that time, and so it would seem that the carb is ok.
B)Bogging down with slow throttle,(in conjunction with A) when hot tells me that she may in fact be rich. So the first go to is sparkplug cuz the plug rarely lies. If she's sooty, swap her out and clean the air filter, and make sure the choke system is NOT ACTIVATED.
C) a bog when you hit it is usually a transition problem. Transitioning from the low-speed/idle circuit to the power circuit. Your only adjustment for this may be the idle speed, crank her up a bit, to just below where the clutch starts nipping at the powerhead.