1. just replace with another 6 speed with a larger granny ring.
2. brifters + 6-7 speeds aint gonna work.
3. ew.

imo, get a nice hyperglide fw with a 30+ granny and a rear derailleur to match. leave everything else the same.

if you want to go the brifter route, then include a new wheelset, cassette, etc and do it with 9-speed.