^ Yeah wound strings are right at their limit at 7-string F.
Conklin sell wound .020 and .022 designed for F
Conklin Guitars Snakeskins Extended-Range Bass Strings you may have to tune DDGGCCFF for a full wound set.
Otherwise contact custom string maker Octave 4 Plus
octave4plus.com i remember that Garry was attempting to make wound strings for above F, they will be expensive like $20 since thin wounds are labour intensive to make. I have one of their wound .018s, amazing string but i don't dare tune it up to F let alone G.
If all else fails, try a thinner plain, the lower tension and thinner gauge mellows and quietens the sound a bit to blend better with the wounds. You can use cheap plain guitar strings if you can find ones long enough (D'Aquisto might be and Rotosound certainly are for a 2+2 headstock), thread an old bass ball end onto one and slide it up against the guitar ball end. I recommend experimenting with cheap guitar plains from .017 down to .014, just keep decreasing the gauge and you might find something you can live with. Problem with a .020 is that, being a thick solid rod, it vibrates with a bizarre 'stiff' inharmonic tone, i don't use any plain larger than .016 for this reason.