I think it will work with the same chain length so long as I avoid the big-to-big and small-to-small combinations. The two chainring setup with the Dingle would give me 42x19 low, 44x17 high and the same overall number of teeth = same chain length. 44x20 and 42x22 on the other side would be the same chain length for those as well, and I think the dropout is long enough and the angle would permit me to flip the wheel around and leave my brake pad adjustment alone. I ran a bunch of numbers on the fixmeup! fixed innovations site and I think I'll be okay.

EDIT: Just went back and ran the numbers again - the freewheel side gears will need about 44.25cm of chainstay length, and the fixed will need about 45.13cm. The effective length I have with the horizontal Huret dropouts is 43-46 cm. It should work even with some chain stretch.