OK, glued the cheek on with a bazillion clamps, cleaned things up and did some test runs. It works. Here, you can see it it in its native habitat (a shooting board) surrounded by lots of end grain shavings (mostly from that red oak board in the background).
Boy, those ramps seem like an eyesore.
Here are some close ups. The end grain shavings, the clean cut on the red oak board and the plane mouth (the cutting edge is to the right). The mouth isn’t nearly as tight as it might look as I used a Japanese style opening, where the top of the mouth is parallel to the top of the iron for the last little bit (one benefit is the sole can be trued a few times before the mouth starts to open. A drawback is it effectively makes the mouth larger than the actual opening). The opening is about 15 thousands of an inch. An interesting side note is that many Japanese planes are bedded around 38º, bevel down, so the cutting action is similar to this plane.
On an another note, the ergonomics of using this plane like a bench plane really suck but it does work good when planeing with the grain. Also, a knob that fits between the thumb/first finger web would probably be a nice addition.