Happy to give things a go myself but if it's less risk getting someone to do it that also works, beats paying what I've been quoted for a new bath and repositioning taps immediately.
You only need borrow a socket, or box spanner, to fit that brass hex, to get it out, long enough to visit a plumbers merchant, to try to find a match/tap refurb kit.
Your rushed plumber, will see more profit to be made, from simply ripping the lot out, and so never even bothered to attempt a simple, cheap repair.
