I'd expect to drill out the trem holes. I expect it was what Fender did rather than get a new trem made just for the Bass VI. But if you can post a pic of the current trem holes, we could give an opinion.

I'd be tempted to swap to slot-headed tuners, as the strings will definitely fit those plus it's a more authentic look. The only issue is they normally require the correct hole spacing to get them to fit with their shared-screw mounting system, and the kit hole spacing is normally a few mm out overall. You can always measure and compare to the spacing diagrams shown on-line for the vintage tuner sets and see what you think. Plugging and redrilling the holes is an option, adding a bit of maple veneer on the front (the tuners cover the filled hole area on the back).

I've used a Dremel with a sanding drum inside the house. A bit messy, but I vacuumed up the sawdust and got away with it.