Hi,
yes this is a common issue when using new 3d-printing services/processes. Some of them end up making the holes too big, some too small.
In your case, and given the price of 3d printing today, the simplest solution is probably to try re-ordering a version with smaller holes, or even a few variations, until you find something that works well for your supplier.
For a solution with less wait time, your method works well, but you have to make sure that the screw is sufficiently oiled before you put it int the glue. WD40 or regular mineral oil should work. Alternatively, you can also try using dental acrylic, which has the possible advantage of not adhering to other materials very well, so it will be less of an issue with sticking to the screw, but i'm not 100% sure on how well it will stick to the drive body either.
best,
jakob