I've done some experimentation along these lines, so I'll share a bit of what I've learned.
I started out with a Jerry Jones Longhorn 6. This has a scale length slightly less than 30", roughly 29 3/4". It comes tuned E-E an octave below a standard guitar, with string gauges .084 to .024, equivalent to the D'Addario XL155 set. It sounds great and plays well except the low E was just too loose for me. I replaced it with a .095 low E from the D'Addario EXL220S short scale set, and it totally works. String tension and tone is well balanced across all strings now. Keep in mind that the Jerry Jones uses standard guitar tuners. This works because the thicker bass strings taper down beyond the nut to a size that fits through the string hole in the tuning post.
After a while I decided I wanted a higher tuning in order to make normal chording less muddy so I got an Ibanez baritone. This is a pretty basic axe with a 27" scale and a single humbucker. The story I heard was that Ibanez couldn't figure out how to market a baritone guitar in the States, so they discontinued this model, strung them up with standard gauge strings tuned up to standard E-E pitch and blew them out through an online retailer. I swapped the strings for a D'Addario EXL158 light gauge baritone set and tune it B-B. The Ibanez humbucker was a bit dark for my taste so I swapped it out for a DiMarzio EJ Custom. Great sound and unbelievably bright for a humbucker!
But now I was missing the low-end rumble of the low E string. It was time to get creative and roll my own and create a hybrid bass/baritone. After a few false starts, I ended up putting a Warmoth baritone neck on a Squier Tele Custom II with a pair of P-90 pickups. I replaced the string-thru-body bridge with a top-load style to accommodate the bass strings. The best I've found is the G&L saddle lock bridge. The pocket in the rear is big enough to hold the ball end of a bass string, though I had to ream out the hole for the low E and A strings. The bottom 3 strings are now from the D'Addario EXL220S short scale bass set tuned to the standard EAD and the high three strings are regular guitar strings. The headstock is a 3+3 Variax style (from another false start) with Gotoh SG38 tuners. The low E string tapers down just barely at the tuning post. If the tuning post and the bridge were 1/8" closer to each other then the string wouldn't fit. If I had to do it again (and I probably will) I would use a left handed Fender style headstock to get as much distance as possible between the low E tuner and the nut. This would allow me to use long scale bass strings which are available in many more gauge choices. As it is, my only choices for decent short scale bass strings seem to be D'Addario and Rotosound. I haven't tried the Rotosounds yet. They've got a .090 low E, so I'm a bit leery of getting too loose with that gauge. But the thicker strings seem to sound too tubby on a short scale bass even though they feel tighter, so the Rotosounds are probably worth a try.
The stock pickups on the Tele Custom II were Seymour Duncan special design, and they actually sounded really good. However, I wanted to separate the high and low strings for stereo amping so I replaced the Seymours with G&L Z-coil pickups with the coils split. The front a rear pickups have opposite windings and magnet polarities so I get some hum-bucking when they're used together.
On the subject of tremolos, I haven't tried them in this application (yet). The Fender Bass VI had a Jaguar/Jazzmaster style of tremolo and Gretsch has a 30" 6 string model with a Bigsby tremolo, so either one seems to be viable. Maybe they both need to use the D'Addario XL156 set with small ball ends. The Gretsch model is called the Jet Baritone, but it's really a bass tuned E-E.