using eight F15T8/BL fluorescent tubes I already own.
For a new exposure system, I would not recommend to use tubes anymore. Product choices have become more limited, and while you now have some tubes, in case you break any, it will become more and more difficult to find appropriate replacements. The alternative, LEDs, is just much simpler these days to implement with easily available electronics. Ready-made LED power supplies are omnipresent and LED strips or COB leds are easy to get also for UV, in varying wavelengths (esp. COB leds).
There's a real difference between today's market and that of, say, 5 years ago.
Having said that - yeah, those ballasts will likely work but I'd prefer to look for some that are explicitly aimed at powering 15W tubes. With ballasts it is NOT a case of 'rated for more power than I will use is probably a good thing'. Tube ballasts need to actually fit the power of the tubes used.
I could not find if your bug light tubes actually allow for rapid cycling; I suspect they don't. If that is the case, I would NOT recommend using them for an UV exposure box at all. You'd be designing a compromised solution right from the start; a waste of time and money IMO.