Mountain bikes of any vintage will get you the tire clearance without even trying, but the weight and typically high trail might be turnoffs. But if you find a high-zoot MTB with butted tubing and have the fork re-raked for less trail*, that could be a really sweet do-anything bike.
* You don't have to go all the way to "low-trail", I'm just envisioning bring it down to a neutral 56mm or so. Toe-overlap isn't usually a problem on these bikes, but doing so would help that even more.