Doubt it is in two gears. Theoretically, the tran's. should lock up if in two gears, thus killing the engine period, and that would be from a dead dig, and stop dead in it's tracks if shifting on the move.
It does sound like a fuel restriction. Did you check for fuel flow from the tank..?? Clean the screen above the sediment bowl..?? If yes, and there is plenty of flow, how about the elbow screen going into the carb., where the fuel line attaches.
An easy way to check for fuel flow into the carb., is to remove the small drain plug from the bottom of the bowl. All carbs. on the 240 had a drain plug, whether it was a Carter, Zenith, or Marvel-Shebler. Let it drain enough to empty the bowl, and see if it has a continous flow after what the bowl should hold.
Do you choke it any when you start it..?? In warm weather my 240, or the Super C's require no choking to start, but all have their own little thing about starting. It really doesn't take much to flood them in warm weather. In cold weather, they are a completely different animal. Choke for about 2 revolutions, then it will run fine, although you may have to feather the choke, until it warms up a bit
On the other hand, do you notice any black smoke from the exhaust..?? Seems strange to need starting flud to start/restart, but continue to run, unless it seems that maybe the governor is kicking in under a pull, when in 4th. Maybe too much fuel, and flooding out, when the governor kicks in a bit..?? Maybe have the proper socket wrench handy at that time to check for wet or dry plugs.
Have you checked the oil bath air breather to see if it is clean, or maybe overfilled with possible water contamination..??
If all of this is up to par, maybe check the intake manifold gaskets for leakage, carb. & to the head. This could be where your losing your intake vacuum pressure.