They won’t coat anything WITHOUT a credit card backing it up, just like other companies won’t do work w/o a deposit.
Unfortunately most consumers don’t take into account all the variables that affect the final price of a coated part. Many thing that most would just shrug off as negligible. Cleanliness of a part and required prep work, masking, blotting, complicated parts, etc.
It just sounds like a mixup so just call and talk to them on Monday. $700 is a little expensive, but is NOT out of the ordinary for similar parts as yours…