Picture Tube Swap

[Electronic M]

How long a CRT will last on a brightener and how much of a voltage bump your tube will need are variables.

I've ran CRTs for months on brighteners and seen no drop off in performance before finding better CRTs. I've also seen CRTs without brighteners wake up on a tester then die in a few months of regular service (the Sylvania 21FBP22 in my Zenith 29JC20 for instance).
If a CRT can produce an acceptably bright picture in the lowest room lighting your comfortable with without a brightener, then there's no need for one. A period brightener will spit out around 8.4V if your CRT doesn't need that much to hit acceptable brightness you can try less and see if it lasts longer...In your set since there's no cabinet I'd run probably run to fail then chuck the chassis on the parts donor shelf.
There's tons of parts chassis out there*, and there's tons of complete sets out there.
*I just liquidated 2 rectangular color parts chassis (the stripped parts take up less space off the rusty chassis) and I have 2 more I'm probably going to do the same to soon.