I recently acquired a Zon Custom 5 and I luuuurve it. I'm keen on trying out some flats for it and curious what y'all recommend. I play Contemporary Christian Praise and dabble very little in slap-funk (trying to learn

)
important specs: 34" scale, low action, 5 string.
***Yes, I've spent a few days lurking thru search functions and reading numerous threads; If it doesn't seem like I have, then .. I'm sorry???***
Ok, well the consensus seems to go with:
1.) TI Jazz Flats
2.) LaBella's
3.) DR ___-beams
I'm very curious and 90% sure I'm going to go with the
TI Jazz Flats, but I wonder...
since these strings are said to have low tension, would it not work well with my Zon (having low action)? I kinda have sloppy technique and I dig in harder than I should most of the time, resulting in hitting-bridgefrets-sound. A cure would be to "pluck up" from what I've read. But aside from that, wouldn't the B-string be mad floppy??
This may sound noob but.... the Zon isn't jazz.. but the strings are... ?
Does that not like.. work?? hahhahha. I don't get what makes Jazz strings.. Jazz. Does that mean they're more dull or dead sounding??
The majority of the ppl who recommend TIJF on these forums seem to have a fretless or recommend it for the fretless, but since mine's fretted,
would Flats go badly with a Zon?? Thanks y'all for reading; Happy Easter!!