So, now I'm torn - should I keep the old battery in there just to see how far it will go or put the new battery in
My .02ยข RM, put the new battery in. Otherwise put the new one, fully charged, in a saddlebag and keep it with you because the old one will fail at the most inopportune time.
Here's what happened when mine failed in heavy traffic one morning.

Most unpleasant.