Update:
With the Dremel it was still quite a bit of work, but the parts now fit.
I'm not sure about the cause of the issues, but I assume the print resolution was not high enough or transparent PLA is not a good material for the job.
Removing material from inside the holes is a pain.
Magnets:
Good news and bad news.
Good news: I managed to put all four small round magnets firmly into the razor - at the ends of cap and base.
Bad news: only two of them are superglued in. I first put the magnets in for fit and orientation, then I failed to remove two of them. the fit is too snug.
So they'll have to stay in without being superglued.
If they do fall out, put a tiny drop of superglue in the hole and re-insert (taking care of the right orientation, ask me for a convenient trick).
In case they fall out and get lost in some shaggy carpet (it happens), I'll include several spare magnets.
The superglue is currently drying and then I'll give the V3 a test shave.