I'd be thinking about a 650b conversion assuming that this measures out OK for that conversion or a different bike with more generous tire clearance. Finding a vintage bike that can take a 35c tire isn't hard; it's a little harder to find one with 38c clearance if we're talking about road bikes. If you really want an all roads bike, an old school mountain bike or hybrid can work well. I did a drop bar conversion on a 90s Specialized Stumpjumper for gravel riding and I'm running 26 x 1.95 tires on it.