Not a shop owner but ..
I'm doing the same thing as the OP. And I flat out told the shop they don't have to match Amazon's price, just tell me what the price is and it'll probably be fine. I've turned them down a couple times but it was because they simply couldn't get a close enough replacement part, not over price.
I can't imagine they make enough on these one-off transactions to cover labor, but they're not turning me down. Sometimes it takes a few days, which if it means they're waiting until the shop person has idle time is fine with me. I just don't want to give any more to Bezos.