Beautiful bass. I’ve spoken to Martin about having a bass built once this whole trade war is over… is this the Elfin or the Elfin Plus?
Anyway, I’m in a similar situation as you. I have a six string headless (and short scale) and prefer flats tone-wise.
I suppose an important question is: are you looking for similar tension, tone and/or feeling as flats, and which flats? Modern like Fender or old school like La Bella?
After much research (reading online, contacting string manufacturers, string retailers, my bass’s bridge manufacturer), I came to the same conclusion as you: GHS Pressurewound or Ken Smith Compression Wounds (same strings). I spoke to GHS and they said they’re fine on a headless.
Another thing to keep in mind is I’ve heard round-core strings are apparently prone to slip too.
The TI Jazz rounds could be an option (if you’re not looking for the tension of La Bella’s Original 1954). They have a round core, but the TI customer support agent I emailed told me he had them on his headless without any issues.