I thought I didn't have the correct eyepieces, but I had another look through my stash of b&l stereo eyepieces and found I actually did have one pair, so I got to testin'.
The first step for both of these is getting a tube lens to go into the camera path. The balplan is arranged with a tube lens in front of the binoculars, leaving the camera path completely empty when the prism is moved out of the way. Fortunately I have a bad head with wiggly oculars, so I took the lens out of it--it is held in with three set screws and is very easy to remove.
I then designed and 3d printed an adapter to take the lens via press fit (its diameter is about 27.75mm) and slide into the 28.5mm trinocular port, with an m42 outer thread.
From here, two approaches are possible. First, you can put the image directly onto the camera sensor by putting empty spacers above the tube lens (ie direct projection). Your other option is to put an eyepiece above the tube lens the appropriate distance so the eyepiece is in focus to the eye, and mount a flat 40mm lens focused to infinity immediately above the eyepiece to pick up the image it produces (afocal). In theory afocal should be the better option on this system since the eyepieces in this system are not totally neutral, and the corrections they apply should improve the image. In practice this isn't always the case, probably because of added aberrations from the 40mm lens. Anyway I tried them both.
Direct projection looks like this. The image does not cover the aps-c sensor, with vignetting covering the corners.
Adding a 1.4x teleconverter gives a pretty much perfectly sized rectangular crop from the field of view, filling the sensor.
Afocal requires a much taller stack. It gives almost exactly the same FoV as direct projection with a 1.4x teleconverter.
How are the results?
Unfortunately my teleconverter is throwing a lens connection error, which is a bummer. So I can only compare a crop from the direct projection image with a resized afocal image. The subject is a wafer, the lens is the 10x darkfield planachromat lit via normal brightfield epi illumination.
Direct projection:
afocal:
Both resized down to 1500 in width for forums posting. There are subtle differences here--the afocal image is a little distorted, just a very slight bulging that's only evident when rapidly switching between the two. Both have similar levels of CA, but it is maybe a little less pronounced in the afocal shot. Contrast is also a little better, though part of that is having to account for different exposure and brightness levels between the two shots. Planarity is similar, though maybe a tiny bit better in the afocal setup. And of course the afocal shot has some artifacts from dust on the eyepiece which I didn't clean well enough.
It may be that the canon pancake lens is adding some distortion or CA of its own here, and hampering the performance of the afocal system. That said, these objectives are achromats and I kind of expect some CA from them in the corners even under the best circumstances. Overall I feel like the image quality is quite acceptable using either method, especially for epi DIC where CA is often effectively masked. The only major downside as I see it is having to dismantle a balplan head for its tube lens.