If you're having that issue on Stingray 4s, then something is off with your string-neck alignment. There is absolutely no issue with the 4s' G string slipping off. Never had that issue with any Stingray (always 4-stringers) that I owned, nor with the 2 that I currently own.
I played a fiver live once, and it was doable, I think I did slip the G once or twice, but technique control and getting used to it would work. Luckily, 5-string basses aren't for me anyways. If I would add a fiver, it would definitely be a Stingray though, tight string spacing and G slipping off be damned.
I will also add, if the string-over-neck alignment is slightly off (be it because of the bridge or the nut or the neck seating in the pocket) - it will definitely affect the fivers more than the fours due to their strings being so closer to the edge of the fretboard.
Another thing - Classic has a fretboard with 7.5" radius which is rounder than the standard fivers' 11". That could also contribute to G string slipping easier off the neck.