Is using an old BB and headset to close off the holes a good idea, or is masking tape a better plan?

I think I’d be slightly concerned about any migration of grease from the old parts.

I think in proper spray shops they use rubber bungs.

I was gonna do just that, leaving the headset cups in but give a good blast of disc brake cleaner followed by alcohol wipe then hand tight a clean bb with spacers on both sides.

YeH, was thinking same.

My an is to hang the frame from the rafters using bolts half threaded into mudguard/brake holes, and sacrifice an old bb and headset to protect headtube and bb shell.

Might even be able to leave the fork in place that way, as that gets painted too.