I've been plalying my JMJ mustang with La Bella 760FS Deep Talkin flats and the sound is that magical thing that a mustang plus flats is meant to do. The thing I never connected with the strings was the feel of them. I've always played rounds and the semi hollow basses I liked the feel of best was an old harmony with rounds but they were old rounds worn in which I liked both the feel and sound. I picked up a pack of the D'addario ECB81M Flats along with the D'addario EXL170 rounds. First tried the Daddario flats and they sounded not as good as the La Bella's but felt pretty similar in terms of feel of the string itself (which leads me to believe I don't think I like the feel of flatwound strings, but do like the sound with the mustang). I now have the Daddario rounds on there which feel wise I am connecting more with and feel more what i'm used to. The town is bright and not what I"m looking for but I'm thinking that after I play them a while they will mellow out and be more what I'm looking for.
What strings would you all recommend for the sound of flats but the feel of rounds with the mustang if such a thing exists?
Well...
Except for a set of TI JR324 Jazz Rounds on my Gretsch Broadkaster, I don't play round wound bass strings any more. They've become just too painful for my nerve-damaged and too-often frostbitten fingers to deal with. I
can play the TI Jazz Rounds, though; they
feell very flat wound-ish, but still
sound pretty much like round wounds. Which would seem to be the opposite of what you're looking for...

In my fairly limited experience with rounds (I've played flats pretty much exclusively for the last 50+ years), I'd have to say that I agree with those who've recommended GHS Bass Boomers and DR Sunbeams. The Boomers are pretty much the
de rigeuer rounds for Thunderbirds; my '13 Gibson T-Bird wore them for several years - before they became too painful to play. It wears Dogal's R44 "Traditional Flats" now. I had Roto 77LD Monel Flats on an '18 Gibson T-Bird; they sounded a lot like the Boomers, TBH. It was wearing them when I sold it... And, I had short scale Boomers on my headless, aluminum-necked '82 Kramer "The Duke", until they just... died. Replaced them with DR Legend flats; which IMO sound pretty much the same, but are much easier on my fingers. And, I had a set of short scale DR Sunbeams on my Warmoth Mini-Precision for quite a while. They did sound very flat wound-ish - on that bass. I toughed it out until they died; then, I replaced them with La Bella 760FS's...
I imagine that there are other rounds that sound sort of like flats, but; I've no idea what they are...
