Have you ever changed the gear oil in the transmission? Might be too late of course, as it could be some excess wear in the transmission itself.
When in third gear, the two shafts (input and output) are linked together as one. While this still utilizes the same two main bearings (input and output again), running it straight through changes the internal dynamics of the trans and it might be putting some "English" on something that doesn't like it.
You should at least check the oil level, if you have not already. Worth a quick shot anyway. And change it out completely if you have never done it or don't know it's history.
And I know you said it sounded like you were lugging the engine, so you obviously know all about that with vehicles, but could that actually still be it? How fast are you going when shifting into third, and what gear ratio is in the pumpkin with what size tires?
Just curious if that's got anything to do with anything or not.
Since it's on the floor, the shifter is not likely to be hitting anything electrical under there that could cause it to run rough in third, but that's actually a possibility sometimes with 3-on-the-tree shifters.
Can't think of anything else off hand.
Good luck.
Paul