Companies that repair/refinish speaker cabinets?

It should come as no surprise that they arrived damaged as the original boxes are only adequate for one shipment and only then if they are strapped down to a shipping pallet. I know, I was the original owner of a pair for five years. 
Besides the marginal packing, the enclosures are fabricated from inexpensive Chinese chipboard and painted. Your best bet is not a woodworking shop but an automotive body shop. You will need them to fill in the dents and dings with Bondo and then repaint them with automotive spray paint. Don't believe me? Watch and report back. 

I'm pretty sure Bondo and automotive spray paint isn't the solution for a high gloss, maple burl veneer, but if they'll provide me with a rational quote, I'm not picky...

You're probably right, particularly if you don't intend to have the repairs done and just want remuneration. If you have maple burl, I believe that is real veneer. My flame red finish, however, was not veneer at all but just multiple layers of paint, most likely automotive. And regardless of that, deep nicks and dents won't be susceptible to sanding and will need to be filled in. Carpenters use wood filler, autobody guys use automotive filler. It is virtually impossible to fill in patches of veneer without it looking obvious. But again, you have made it clear you won't necessarily get the repairs done which makes me think the damage must be relatively minor. I am sorry this happened to you. When I sold mine, I hired a guy to drive them to the buyer several states away. It was the only thing in his small pick up. Pricey, but one way to insure damage free delivery.