Man, I hate to even wade into this one, but alas as a moth to a flame

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The Golden Wildbeeast mount didnt look too bad, actually. Clearly the wrong horns which maybe belonged to the OP's blue wildbeeast as someone suggested. I've gotten shipments from places with little info on the horns to ID which cape they belong to- such as multiple Springboks together. I do ask for pictures to try and sort that out.
As for wrinkles in the armpit, News Flash, they are there in the live animal. The anatomy of some of the taxidermy forms makes them more glaring on occasion, but "stretching them out" ie pull it further back is not the correct answer either.
The fact your new contracted taxi can regrow hair (If I could do that I'd be a billionaire

- sorry old taxidermy joke). Blend with paint to try and camouflage the bare areas, yes, but that invoice shows on a kudu, which is known for its bare spots anyway. BTW, maybe I missed the pics of the kudu mount....
Getting the lips retucked is a POSSIBLY, depending on what type glue was used, and much much work the new taxi wants to get involved with.
So in the end $315 for a new paint job, which isn't going to address what you and they consider the actual major flaws....... lips, wrinkles, eyes etc
Of course none of this excuses the business practices you have encountered.