My experience is that a lot of independent mechanics will do what you ask them to do, so long as they think it’s not unsafe and have confidence that you’ll pay the bill without complaint when the task is done whether or not the problem is fixed.
Probably not a good “this is my first time meeting you, but please replace my flux capacitor” but if you’ve got a history with the shop, I’m surprised you couldn’t talk him into it. (I worked in a shop briefly in college. We’d do what the customer wanted, including installing parts they bought, but the only warranty was on a “we spent an hour; you paid for an hour; thus ends the transaction” basis.)