I'm the same way, i have big hands and long "piano fingers" I stumble over myself on the lower notes of a jazz neck. I like wide flat fretboards and meaty necks. My P-bass has a maple fretboard mighty mite neck that is awesome and fits my hand great, one of the most comfortable necks i've played.
Kinda OT but I got a question for you, what kind of guitars are your guitarists running? I'm trying out different tunings for an upcoming project and the lowest I've gotten with any intonation stability is Drop G on my 27" Baritone Jaguar. I've run out of room for saddle adjustment on the low G so I'm stuck there. But I'd love to mess around in F like you guys do, and I'm afraid I'm gonna have to keep my eye out for my elusive white whale of a guitar, a Fender Bottom Master, its basically a 28.5" scale baritone jaguar, with black hardware and different electronics. It's supposed to be able to be setup anywhere from baritone to bass vi tuning so that would work, but their impossible to find (I'm having a hard enough time finding a backup Baritone Jag).