Run in the manner that the Quickie operates, I would expect no less than 10,000 hours of lifetime, with the upper limit being pretty difficult to determine.
FWIW, I have a pair of used old stock Sylvania 6SN7's that have been in constant service for nearly 4 years now (never turned off) that still operate properly and test good. That is 35,000 hours. Consequently, I think I will be selling off quite a few of my 6SN7's, as a lifetime supply won't be that many tubes.