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...the only thing I can think of given your story, that you got the thing rethreaded but still can't get the correct BB replacement unit from Velo Orange to install, is that maybe your BB shell is a little bit ovalized. It's not that uncommon in production bikes.

Chasing the threads with a tap pushes the BB out round again while you're tapping it, but it usually goes right back to oval as soon as you remove the taps, because you've not exceeded the elastic limits of the steel BB shell. If that's the case, you can usually determine it by using a Vernier caliper to measure in several directions inside the BB, and see if there's variation.

The simplest and cheapest solution is to carefully get your sealed unit BB replacement started in straight on both sides, and then use brute force to thread it the rest of the way in on both sides. I've done it a couple of times at the co-op on cheap Chinese bikes for people who had no other alternatives, but it's not the ideal situation. If that's the problem, and you decide to go this route, use plenty of grease on the threads before you install the unit.