Success! A 1:1 transformer (Triad Magnetics VPS230-190, a 43W transformer) worked much better than a step-down followed by a step-up transformer.

I hit 166VDC at 110mA. I did some more science to get power losses.

A few interesting things. First, the 1:1 transformer isn't quite 1:1. In fact, turning the transformer around got me only 127VDC, so I have to keep the orientation correct. Second, there is between 3.6W and 4W being lost in the transformer. Finally, the power lost in the rectifier/capacitor is 1W at the low end, and 6W at the high end.

The inlet I used (Delta Electronics 06AK2D) is an EMI filter, switched and fused for 6A.

With the power circuitry decided upon, I can finally get to the business of testing the Nixie driver board.