Could be one or more of several things- but the H jet has little to no bearing on the transition from idle to WOT- that is the domain of the L circuit of your carb.
H controls how much or how little fuel is available to the compression area when the throttle is already at WOT, for the initial from idle to get there is L and it sounds like the simple fix for your saw might be to lean (screw in the L jet) a small amount and try for throttle response, base setting should be close to 1 full turn or 1 and 1/4 full turn out from lightly seated.
But it could lots of other things fuel and or fuel delivery related- like water in fuel, bad fuel, gummed up carb, stiff diaphragm, leak in fuel line, blocked fuel filter, poor impulse........