This problem with short top tubes, or more commonly with top tubes that are effectively shortened by relaxed seat tube angles, is the reason that I, at just over 5'9", prefer larger sizes when selecting from both the older and the cheaper bikes that so often have touring angles.

These are set up for the hardest riding that I can dish out here in the foothills, the Clubman (with 71-degree seat tube) feeling if anything a little small in the top tube, and the Kokusai (with 72-degree seat tube and longer top tube) feeling a bit long in the top tube.

The Sachs is actually good in the top tube reach dimension, but I'll need to use a track stem to lower the bars another inch.