The gear box is literally a gear box. So you're not going to get hesitation from that. The gears either work, or they're broken. Not much room for middle ground.
So today, what I did was adjusted the drive-engagement cable, pulling out all the slack. Basically, I slide the housing down through the clamp that holds it, so its a much firmer pull. This was the first thing I did that had SOME effect!!
NOW, 1st gear works pretty good. 2nd and 3rd work about as good as 1st before. That is, not great.