Vendor charging me $850+ in unrequested "overtime" after our wedding—am I crazy or is this ridiculous?

Hey everyone, looking for a reality check / advice on a post-wedding vendor dispute.
We got married recently and hired a live string trio for our ceremony. Overall, the music was lovely on the day of, but the interaction with the company owner afterward has left a terrible taste in my mouth. They also keep referencing that they’ve done thousands of weddings and no couples ever given them problems about paying for overtime and they’ve done so within a day of them asking.

The Background & Contract
Our contract with the vendor ran for a 1-hour ceremony package with a contracted end time of 3:30 PM (for music)
Here is the exact clause regarding overtime from the signed contract:
"Should additional time be specifically required or requested directly from the couple and mutually agreed upon by the musicians on site, an additional fee of $250+HST per musician per hour (minimum) will be added on to the total service fee and charged back to the couple following the end of the wedding for any amount of time past the time stated for "End of Services"."

What Actually Happened
Neither my husband nor I ever asked or authorized the musicians to stay past 3:30 PM.
The ceremony ran slightly over—recessional wrapped around 3:45 PM (we have time-stamped photos of us in our car leaving for our reception venue at 3:45 PM while guests were still leaving).
The musicians ended up staying until ~3:47 PM and took until 4:00 PM to pack up their gear.
The company owner emailed us the day after the wedding demanding an extra $847.50 ($250 + 13% tax × 3 musicians) for 1 hour of overtime.

The Response & Escalation
When I politely pointed out Clause 3 and noted that neither of us requested or authorized overtime, the owner sent a massive rebuttal admitting that he/she instructed the musicians to stay, not us.
In the email, the owner:
Shared WhatsApp screenshots showing they told their musicians to stay on site past 3:30 PM.
Stated that their violinist had another gig booked right after and was running late for it (meaning they booked back-to-back gigs with a 15-minute window in a major city with zero buffer time).
Made passive-aggressive comments about our finances, saying "If your wedding budget was tight, I totally sympathize and understand" and offered to drop the fee to 30 minutes ($423.75) out of "kindness."
Claimed that their contract states "if the finished time ends after the stated time, we charge a minimum of one hour"—which is completely untrue and explicitly contradicts the actual written contract text requiring a direct request from the couple.

Where Things Stand
It feels like the company owner made poor operational choices (booking musicians with zero buffer time between gigs) and internal management decisions (telling their contractors to stay without asking the clients), and is now trying to guilt-trip us into paying for their own scheduling mistakes. Paying $850+ on top of a 1-hour performance package for an unrequested 15-minute overrun feels completely unreasonable.
We mentioned that the contract didn’t state that and that they did not stay till four like they said, and they came back with all this rebuttal, but then said they would accept 50% of what they’re asking for
We plan to send $423.75 as a voluntary "full and final settlement" purely as a goodwill gesture for the 15 minutes up to 3:45 PM just to close out the account, along with a firm boundary to stop the guilt-tripping and unprofessional comments.
Has anyone else dealt with a vendor trying to enforce "automatic overtime" that wasn't in the contract? How would you handle this?