Low tension flatwound or tapewound strings?

I recently picked up a cheapo Asian-made Höfner Club Bass for next to nothing, because the top has started sagging underneath the bridge - the two layers of the laminted top had separated there, I assume it might have got hit on the bridge or sat in a case that wasn't tall enough.
At any rate, I tinker around with guitars and basses a lot, so I used this opportunity to test my repair skills - wicked in some glue between the separated plywood layers, and glued a layer of maple veneer as a kind of bridge plate to the inside of the top - seems solid now...
But still, I don't want to take chances, so I'm going to use lower tension strings; the bass came with roundwounds (which I hate) - on my Precision I use D'Addario Chromes flatwounds, not sure what to use here?
I heard Thomastik Infeld flats have less string pull than other brands? What about tapewounds? Never tried those, how's the string pull with these, compared to flats? LaBella makes those in medium scale (which I need for the Club Bass). Other options for low tension strings?
BTW, the tone I'm shooting for is a thumpy, upright-bass-like old-school tone (I only use the neck pickup, and pluck the strings near the end of the neck).

 

Their JF324 set (which seems to be the right one for my bass) is around 45 Euros, don't know what they cost elsewhere - about the same as LaBella or Pyramid flatwounds, a bit more than D'Addario. If I put those on, the value of that bass will rise almost 50%...

 

It's basically a tone thing, not a feel thing, I like those deep, thumpy tones, the Stax/Motown Duck Dunn/James Jamerson tone, which I get with my Precision with flats.
I got the Höfner for upright bass-like tones, for playing with an acoustic group, folk/country/Americana-style music ("from Hank to Lucinda Williams") - I think, flatwounds will get me much closer than roundwounds there...
I used to play Rotosound roundwounds with a pick in my young punk/grunge days, but that was a loooong time ago...

 

I do realize that for a given string gauge, type, and scale, the actual tension (as a scientific property) has to be the same every time, to be at the right pitch, and that this is different from "perceived tension"/feel/slinkyness, whatever you want to call it (I actually got into a big discussion on TGP about this a long time ago) - BUT: I believe that differences in construction (esp. round vs hexagonal core, different alloys of core and windings, etc.) might result in a different required tension for various strings, even if they have the same gauge? After all, eg. a round-core .040 string is going to have a different (higher) mass than a hexagonal core one of the same gauge, so it should require more tension to vibrate at the same pitch.

But we're getting slightly off topic here...

BTW, I haven't checked - but do medium scale Chromes also come in lighter gauges?

 

I rarely ever check into TDPRI these days, and on TGP I'm usually only on the Alt.Country-mega thread. But I do want to start playing bass a bit more again, so I'll be around here, too...

 

Those look interesting, but all the dealers I checked only have them in long scale...

 

Great sound, but 65-115 gauge might require a bit of work on the nut - and I'm not sure how much string pull they have (as I said, I'm looking for something with less tension - no experience how tapewounds compare to flatwounds there...)

 

Unfortunately: "Non-Standard scale sets (Medium, Extra Long) are not available to purchase on www.LaBella.com. Please see drop-down of “Trusted Online Retailers” below the product image to locate one of these sets." (from the LaBella webpage)