The only possible leverage he could have had would have been to try to get Gates and Jobs into a bidding war. But that only works if Microsoft sees it as a competitive advantage to have the switcher for their apps but no one else's.
And, like you said, Andy already admitted he wanted it on all Macs, which blew any chance at leverage he had.
It's hard to say, because we weren't there. But I would have just said, then and there, "bullshit, I'll talk to Bill" and walked out the office - 10$ says he wouldn't have made it to the exit :)
Times were different back then. The market was nothing whatsoever like it is today. The context of this was for applications microsoft was writing for the mac, not for operating system development... and the fact that he had insider knowledge could have been used against him. And $100,000 was a decent amount of money at the time.
And, like you said, Andy already admitted he wanted it on all Macs, which blew any chance at leverage he had.