Hi guys and gals, (if this is TLDR, skip to the last paragraph

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I am a upright player who is somewhat new to electric but not so much to fretted instruments (jazz guitar). Anyhow, I bought a LTD (ESP) B-206SM for myself at Christmas this year, and I love it. I am now getting to the point where I would like to replace the strings. The pre-installed strings were SIT, and they are ok but I would like to try some other options.
I am leaning towards flats because I am playing primarily jazz, groove oriented stuff, and generally prefer a warm, round natural sounding bass tone (not looking to sound just like an upright, as that is impossible, but I'm not really into super bright electric sounds). I had a set of Chromes (4 string) on my old kicker and put them on the middle 4 strings today. Perhaps they need time to settle, but the tone is pretty much what I didn't like about chromes on any of my guitars - bright, lacking warmth and depth.
I have always gone with TI flats on guitar and love the tone (also love their roundwound tone - double nickle wrapped). I'm looking on some input on those, but they're like a hundred bucks, so buying them to find out they are too muddy or something would be disappointing, and money is a bit tight now. At the same time, Once I put them on guitar I never take them off because they just keep sounding better, so I would not have a problem if I knew I would use them.
Any opinions on the TI set? Also, is there any sort of roundwound option that might also get that kind of warm and deep sound? Any other flats that I should be considering? Luckily these prices are not anything like upright strings, but still money is tight now and I am working with this bass more than other instruments these days, so I would like to tweak my sound. I would love to buy a bunch of sets and try them all but it won't be happening for a while, too long to wait.
Thanks for any advice, I really appreciate it if you made it through all of that!
e: Also, playing mostly in a piano trio, so having a tone similar to a guitar, as is said with round wounds, is not too big of a deal, if you have rounds to recommend.