I have one of the first generation G5265s (29.75" scale). Did not care for the stock mini HB PUs and swapped them out for a left over set of
short pole "budget line" DeArmond 2000s, used on many Gretsches in the 1990's & early 2000's Korean models. Clearer and better low end, more surf spank when needed. Used foam or neoprene rings (like on a Rickenbacker 6 string) for height adjustment.
Added a dual concentric pot for a master volume & tone (the other two are Neck/Bridge PU volumes).
They originally came strung E1 (later via Gretsch in B).. the extra length required due to the Bigsby will cause some sets to be too short (usually the 3rd & 4th string).
The stock strings were Fender 5350 Bass VI (25-95).
I currently have it tuned to A (I believe I have Pyramid "Gretsch Baritone" strings on there now (14-72), brass ball ends, they are very long between 125-130cm).
The D'Addario EXL157 (14-68) & EXL158 (13-62) should just fit for the 3rd & 4th strings (just held those two up to check).
When I was still using it for E1 tuning, I made a set of flats using single Pyramid Gold flats, using individual strings intended for different scale lengths to get a full set. Worked out well (unfortunately I don't remember what I used, it was years ago - I went by the measurements which Pyramid published & it functioned).
The current Pyramid VI Flat wounds (25-85) are listed as having a "Total length: 100 cm" (39.37") which might just fit, but will be very tight on the 4th & 3rd.
You
can swap out the Tele type top mounted Bigsby (not my favorite type, but it works) for a hard tail (or perhaps a Gretsch trapeze tail piece - if the break angle is enough... haven't tried it); HOWEVER, it will leave you with 6 holes in the top to deal with (5 Bigsby screws & the ground wire).
The old G5265 is definitely not a top end instrument, but it is still very playable (with a bit of fret end smoothing) and fun (albeit a bit heavy, despite the basswood body). The Corts and even current Squier baris are probably better, but the 29.75" scale is nice.
You can still often find them used cheap as chips. I believe the newer models are a bit better build quality and available as hard tails e.g.the G5260 EMTC Jet... same old top mount type mini HB PUs though). PUs with DeArmond & Rickenbacker HiGain/Toaster formats should fit without too much trouble, with a bit more routing work, P-90s (or other mini HBs in a P-90 conversion ring) could be fit. GFS & Roswell both have top mount PUs in these sizes. TV-Jones also has DeArmond mount models for most of his PUs... but they would cost more than a G5265 new ....
Here 3 of my 4 Bari siblings, left to right: Gretsch G5265 [29.75" scale], Cort Sunset [28.6" scale], Fender "Modern Player Plus" Telecaster (CIC) [now 27.96 scale] with a (bought used w/ the water slide logo..) Gödo baritone conversion neck (was a bugger to fit since in CN the original 22 fret neck used a deeper neck pocket instead of a FB overhang, had to fill the base of the rout with a maple extension). The other is also a Gödo Tele Conversion with 2 CC PUs, but in the band room not here, so no pic: