PREFACE - I am new to this, so my opinion is not worth someone who has done more of this.
However...
First thought - $770 in halves is 1540 coins... my first dump (from collecting pennies for no good reason for almost 10 years) was almost $80 in pennies... or 8000 coins... over 5 times the number of coins you are looking to dump.
Second thought - Even though the bank I dump at is a national bank that screwed my wife and I over years back, I realize that the people who actually do the work for me when I dump had nothing to do with that, so I always try to be polite with them. And at least at this bank, the main thing is coming when they aren't busy. I usually give them a call and just say "hey, I've got $100 in dimes I need to cash in, would now be a good time?"
Third thought - assuming that you do try to go when they aren't busy, I would think splitting it would be MORE of a pain in the ass than doing it all at once. Either way, at some point they will have to switch out bags and get 1540 coins through the machine.
Third though - Best thought yet - why not just give the bank a call (since it might help to do that to see when they are busy anyways) and ask them what they would prefer...