Question: if I have a 10-and-5 guy who won't accept a trade to another team, can I get around that by involving a 3rd team?  In other words, if he'll accept the trade to the 3rd team, that should erase the "5" part of the equation, and that 3rd team could then trade him to the originally intended target, no?

He'll only accept a deal to a better team. 

What I assume you're proposing is to involve a better team, move him there and then have that team move the player to the team that actually wants him.  Yes, pretty sure that would work.    Sounds a little underhanded though so you should tell the world what you're doing as it will take multiple deals.

Thanks for the answer, and yes, that's what I was proposing.  Not sure how far down that path I want to go, though, if it's something that a lot of other owners would find unethical.

If the deals are fair, there shouldn't be much complaining.   In MLB, they'd just negotiate another year on a contract to get a player to drop his NTC.  We can't do that.  So you're seeking an alternative.   But I'd make sure everyone knew what was happening just in case.