I don't think I've seen baritone gone past B on a Fender-scale electric. I think you'll have problems with setup and intonation, but low tension, not high, will be the crux of your frustrations.
For strings, take a standard (heavy) string set and toss the high E string and ... I honestly don't know where to go for a thicker nylon/gut string, but you should be able to find singles at a string outlet like Just Strings or maybe your local shop. I'd say .053 or so would get you in the ballpark.
(Ironically, early rock guitarists would get standard (.012s) sets, toss the low E, get a thin banjo string and that's how we got the .009s we do often use these days.)
As a former fretless guitar owner and current steel guitar and slide guitar player, sustain is the best friend I have when working without frets. My suggestion for fretless guitar is an electric with a humbucker and maybe a Sustainer or the like. Either way, guitarists come up believing that intonation is something you set with a screwdriver, not something your ears and fingers work out. It took a long time to get to my current state of mental intonation, and unless you come from a strings (violin, cello, etc) background, that will be your learning curve as well.
Part of me thinks "look into Ouds; they're built for this sort of thing", but I hope you find the sounds you want in this journey.