I don't see the rational for that original setup. It's not a real half-step. The incremental ratio of the cluster is 1.15, so the ratio of the chainrings should be 1.075. Then the crankset would have been 52-48.

A half-step for a 52/45 would have been an increment of 1.30. Starting with 14 teeth, 14, 18, 23, 31, 39 would have been the (infeasible) rear end. Starting with 13, 17, 22, 29, 37 is equally unsuitable.

Maybe it's an alpine? What happens when we try an incremental ratio of 1.05? 14, 15, 16,17, 18, 19 - narrow range but build able and the steps are even. It also could be 13, 14, 15, 16, 17, 18.

My guess is most likely the crank was planned for a 5 or 6-speed straight-block, or corncob. But the lowest gear (45/18) is only about 67 inches, so it is pretty much a racing only gearing.

Basically those numbers don't work well together.