A potential problem in this case with using a auction with multiple bidders: it could reopen the domain ownership dispute.

By my (admittedly limited) understanding, demonstrating you are not just interested in flipping a domain to the highest bidder, but have a valid intended use, is one of the factors that can overcome a trademark claim.

As in many questions asked here, the poster really needs to find an expert. I would suggest someone whose business is domain buying and selling, including in the presence of trademark claims, and get their negotiation advice (perhaps for a commission).

(Sorry, no names come to mind. There was an article about some successful speculator/squatter in Vancouver a couple years ago...)