For what it's worth, featherweights at heavyweight events aren't really weighed. There's a good deal of leeway as the meleés are just for fun so no-one is going to be nitpicking if it's a few grams overweight (or even a few hundred grams, unless there's a competition run). Hopefully this will free up some time for you to put towards the drive issues.

Is there any side-to-side wobble on the wheel sprockets or motor sprockets? This will be a contributor to throwing chains, with the other one being the sprockets mounted eccentrically (not concentric to the shaft) so that the tension will increase and decrease as the wheel rotates. It's a difficult thing to get right without decent tooling. The side to side wobble can sometimes be sorted with strategically placed washers, but eccentric mounting is harder to rectify. Having chains really tight isn't good, you want a little slack in them but obviously this is exacerbating the problem too. Not much to do except keep plugging away to find the right positioning that gets it working