Bummer, I feel ya. My lathe has been down since spring, right until this past weekend. Long convoluted story which I will document, but I'm cautiously certain its fully resolved now & hopefully much better than it was new. TBC
You might get some help from BB if you politely contact the right people & mention/reference your public post. I haven't heard great things about BB support in other forums but sometimes its location or person or time specific. At minimum maybe they can endeavor to send out some more electrical components to swap in vs. the conventional order/hope/wait routine. I have also read posts with BB specifically when someone digs into the machine & determines that the physical wiring does match the schematic in their manual. So that would be another good conversation starting point is give them your serial number & ask for schematic. At least then if you know an electrical savy guy he has something to work off to do basic component checking.
If the conclusion is that BB electrics are just too flakey & the lathe is otherwise desirable to keep then maybe consider VFD as suggested. Here I have zero practical experience except internet lurking & its your money & time etc. But it seems to be a common thing that people are successfully retrofitting, not just to bypass problems but to get some worthwhile advantages. The cost, brands, programming seem to vary all over the map but from what I can tell its the same end result - swap in motor, hook up magic box with separate cable & it essentially bypasses everything electric in your lathe. Maybe I'm wrong, but that seems worth the effort. If it works you are home free with a better machine. If it doesn't, you probably haven't violated the base machine with new holes or uprooted wiring to the extent its worth less to sell. The ultimate bailout would hopefully see you recover decent % of VFD if it had no other application in the shop. At least that's how my brain works.
There is a ton of VFD information out there, 99% above my head, but I'll suggest 2 references.
1) Stefan Gotteswinter with similar size lathe as yours
http://www.gtwr.de/shop/pro_mykrodreh/index.html
2) Basement shop guy on YouTube where he has VFD'd older gen USA iron & shows some of that.
https://www.youtube.com/user/BasementShopGuy
VFD talk around min-13