The expensive but elegant solution is as follows:
Get a set of 15" splitters, send them to Stockton Wheel and have the centers mounted in a more modern 16" rim, with the backset that you specify. Then use a set of truck type tires like the Yokohama 750x16 that have a skinny 5 1/2 " tread, or something close to that. This way you have a very original look, with modern one piece rims and the original hubcaps.