They do settle down- I played a wedding on the beach tonight in cape cod, and I didn't need to tune often- I checked at the beginning of each set but they were very close each time.
I also haven't played my regular electric on a gig since I got my rondo solid body. I have a 31" scale 6.5 lb birdsong that is beautiful and sounds amazing, however my arthritis is making even that one hard to play, and the uke bass is so easy that I'm probably not going back. 4 lbs and 21" scale (23.5" when I can finally get that 5 string, very soon!) is really working for me.
Tell your husband that the biggest adjustment is to fret in between the frets rather than at them as you would on a traditional electric bass, and while the rubber strings can take a hard attack, they're better with a lighter touch. I had to remind myself of that during tonight's gig...