I have GHS short scale 32.75" windings BPN's on my 30-inch scale travel bass. It has a standard plate bridge. The windings taper to silk between the nut and the E-string tuner post as they should. No issues. If the winding/speaking length of the string does wrap around the E-string tuner post, and you are concerned, post pix of the bass, bridge and headstock and we can suggest remedies.
^This^ I've been playing short scale basses for... well, a long time, now. Long enough to know that all short basses are
not the same. And, long enough to have found out the hard way, that all short scale strings are not the same, either. I have a set of short scale TI Jazz Rounds on a 30.5" scale Gretsch Broadkaster. It's a bass that is simply physically too big for any short scale strings but the TI's; is too big for a lot of "medium" scale strings; but
will happily wear long scale strings all day... I also have a set of short scale Dogal R45 'Traditional Flats' in my string stash - that are too short for all but one of my short scale basses - a headless, '82 Kramer Duke, with tuners behind it's Schaller roller bridge... On most of the others? The Dogal's don't even make it to the tuner pegs. However...
I use the GHS #3020's on... 3?... short scales (10 of my 27 basses are shorties; it's hard to keep track) and TBH, I can't think of any other strings I use - or have used - that fit your description. La Bella 760FX's might; but, at 39-96 gauge? On my Dano Longhorn, they're a little "twang-y"; but that's the "Dano Sound" I want. On a different bass? Depends on the bass, I'd imagine... All my other shorties wear heavier flats (43-104 or heavier), except for the violin bass that wears Roto TruBass 88 Tapes. The Kramer Duke is currently wearing DR SFL45 flats; mainly because they sound a lot like the 50-107 GHS Boomers that it came to me with. But, although they are 45-105's, they are
round core flats; which most flats are not. I don't find them particularly flexible on the Duke, but; they ain't exactly bridge cables, either. They might work for you - or they might not...
So... I'd say stick with the GHS 3020's, if they make you happy. And if they'll fit that new bass. Otherwise? I think you're in for some experimenting. Good luck...

So... I'd