If I get a registered, taxed, paid-in-full SBR, and then want to get another upper, also SBR, for it, do I need to the SBR paperwork/taxes again, or can I just show them the paperwork on the rifle and be good to go?
There is no paperwork requirement on "SBR" uppers.
You cannot possess more SBR uppers than registered lowers, unless you possess zero AR-type lowers. In other words, if you possess one SBR lower and no other AR type lowers or rifles, you can possess more than one SBR upper. But otherwise you cannot since you "could" put together an unregistered SBR-- that's where the BATF's "constructive possession" comes in.