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I purchased a B1C flatbed a few months ago, and I am going through some of the same stuff that you mentioned.
Are you sure you have a B2B? That would make it a half ton truck. Usually the duallys were one ton and bigger, weren’t they?
Anyway, about your questions:
1) The 12V conversion is pretty straight-forward. Alternator, 12V coil, ballast resistor, 12V bulbs, put a resistor inline for the fuel gauge and any other 6V items you want to keep like the heater fan, etc. www.vintagepowerwagons.com has a kit. Check out their kit online, then buy your own components (cheaper that way). Starter still turns the same way, only faster.
I used a Mopar alternator on my truck (fits good) Other guys have used the Chevy alternator.
2) Not sure about the problem with your rims. I’m running radials on original rims on my truck.
3) Pilotthouse trucks had electric wipers as an option. The 6V wiper motor can be updated to 12V by a competent repair guy. I know a guy here in the Cinti area who advertises these types of conversions in the street rod mags. Personally, I used the Newport Engineering 12V wiper kit in my truck.
Good luck with your new truck. You will find all kinds of answers available by searching the forum. Email me if I can help
Tony