Escalate Monk and threaten legal action if needed. They have insurance to cover mechanical mistakes by their workers. Most auto repair places work off the same "Script":
#1 Deny
#2 Deny
#3 Deny
#4 Accuse the customer
#5 Lie
#6 Deny
And on it goes. Your best case is to:
#1 Talk to the local manager and attempt resolution
#2 Have a different mechanic verify (and document) that the battery is old. Many batteries have date codes on them.
#3 Talk to regional manager. Casually but firmly mention that you do not want to pursue legal action, but you are prepared to do so if a fair and reasonable resolution isn't achieved.
#4 Talk to a national headquarters. Legal action still on the table.
I would also add up every penny their negligence cost you and also calculate an amount beyond that for the inconvenience they caused you.
"We're just two lost souls swimming in a fish bowl -- year after year..."