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 .02¢ 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.