Okay...
Yeah, TI Jazz Flats are not the best strings for what you want to do with that bass. I have them on my Alembic Epic; which is the bass I... try... to play Jazz on. Being well aware of their... flexibility... this bass is finger-picked only, and while I don't play slap style at all - I would definitely never try it with the TI's. As for trying the Fender Flats? I would definitely replace the TI's with a set of 9050L's. Mainly because, aside from fixing all the drawbacks you're having with the TI's? Fender 9050l's
sound an awful lot like TIJFs. I've had the Fenders on several of my basses over the years, and still have them on my G&L ASAT Bass. As I said, I don't slap - but I do play with a pick about 98% of the time. The Fenders do that very well...
As for the Semi-Hollow? Yeah, you're not going to get what you want, from arguably the brightest flats around (although, EB Slinky Cobalts
might be a hair brighter). Sadly, the 9050's don't come in medium scale, or I'd recommend them on that bass, too. I've had them on one of my long scale semi-hollow basses (a 1st Gen MIK Danelectro DC59) for years. They were plenty thumpy on that bass, but... not
quite what I'd call Old School. But, if that's what you want? La Bella DTF's will definitely give it to you. But, I wouldn't recommend the ones you mentioned. The FHBB's are expressly made for Beatle Basses, with small ball ends (Hofners sometimes struggle with normal Bass string ball ends) and a very long, small diameter tuner end to work with the guitar-style machine heads on Hofner's, and some other basses - like some models of Danelectros. Regular medium scale 760FL's should work just fine. As For the GHS Precision Flats? I have the long and short scale sets on two basses (both solid bodies), and I definitely like them - a
lot. I like them so much, that as soon as I can get off my lazy butt, I'm going to put a medium scale set of them on my new Guild Starfire I - a semi-hollow body bass. And, as for the Pyramids? I was going to put a "short scale" set of them on the Guild, but... they are just a hair too short for that bass.
So... yeah; if you want Thump from the ABG200? La Bella 760FLs, or GHs Precisions will definitely give it to you. But, I think I'd take some measurements first - from where the ball ends mount, to the nut - to make sure that medium scale strings are what you need - and which ones will actually fit. I have basses that'll fool you - including a short scale Gretsch
bass that really, really likes "long scale"
strings...
Oh... as for the "flat/dull E string" thing? Speaking from 50+ year's experience with flats, I'll tell you that, right out of the package? A "Dull/Dead" E string - and "Bright" A,D, & G strings, are pretty much the norm with brand new flats. Flat wound strings need to be played - sometimes a little, sometimes a lot - to break them in. As you play them, the E string will brighten up, as the other strings lose their brightness. When they eventually meet somewhere in the middle? They're now broken in, and they'll stay like that for a long time...