Can Small Bolt spindles run Big Bolt rotors?

Yes, the spindle on the late model drum brake knuckles is the same as on the disc brake cars. So all you need to do is slide a big bolt pattern rotor on the spindle. You'll have to use a special bracket to mount the caliper though. Doctor Diff has this stuff if you want it although I think a better solution is to just swap on a set of disc brake knuckles.

Here is how I did it 20 years ago. Late model A body drum knuckles, custom adapter plate, Viper calipers, and 11.75 rotors from a B body. It all bolts together. Worked pretty good too for some wrecking yard engineering.
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The only issue I see with all of this is that you’re assuming he has late model drum spindles. He said he has BBP drums, which means it’s possible he has pre-‘73 B or E body spindles. Which use different bearings than the 73+ stuff.

I’m just going off the OP’s post, if he has BBP drums then he doesn’t have A-body drum spindles.