In my mind, the only reason for going from a 5/8 to an 11/16 bridge, assuming you have no buzzing or other problems with the 5/8, is so that you WILL HAVE a slightly higher action. This often allows for more volume, better, snappier pull-offs, etc.
Slip a popsicle stick, they're 1/16" thick, under your current bridge so your new height becomes 11/16" and see if your fingers like it. Keep in mind that taller than 5/8" could cause finger and/or hand discomfort for some, but definitely not all, folks.
I play a Nechville with a 3/4" bridge and love it. One of my students wants to try raising his bridge height and I'd also like to put a compensated bridge on for him. I have a bridge which will be ideal, I think we'll just have to give it a go and see how it works out. We can always change it back if not :-)
Yeah, it changes the angle of your hand. Especially if you are somebody who just has to keep 2 fingers planted on the head "like Earl did". But if you like playing with no fingers planted, or occasionally just 1, it should'nt be a problem.
I'm glad you mentioned that. I've only ever been able to plant my pinky. However, my pinky is very short and of late I have stopped planting altogether. I find it helps my playing to have that freedom of movement and it gives my banjo a more open sound. It also means I can experiment with playing on the lower strings of the banjo. I'm sure I would have made the decision years ago if it hadn't been for the all pervasive view that you "have" to plant.