John,
Again – all input on the subject appreciated!
I've not tried anything like you have here (you come up with some great stuff!

) , but in a couple of ways have a little experience with "stopping down" microscope objectives when used on a microscope.
First would be using the older Nikon objectives made for their "Universal Stage". These are long working distance and they actually have an adjustable aperture built into the objective. (Apparently this was needed for some function using one of these exotic universal stages). In any event, my experience was that just about any amount of "stopping down" was clearly noticeable in a reduction of resolution. The second case is with more modern, high quality, high NA microscope objectives that also have a diaphragm built in for slightly adjusting the aperture to achieve proper darkfield illumination with dedicated darkfield condensers. Here again, it was very obvious that if I accidentally "stopped down" in brightfield illumination I could clearly see the reduction in resolution.
The third case was when I added a slightly smaller "waterhouse stop" (simply a black mask with a circular hole in it) to the back of my 20/0.70 S Plan Apo. This was done to see if I could get better results in darkfield, since the high NA of this objective (for it's magnification) made darkfield with 3-dimensional subjects very difficult (huge out-of-focus areas that were brightly illuminated). This actually worked OK. It did seem to reduce resolution a little, but it also helped a great deal in "shrinking" the huge OOF areas. (In the "old days" there were little devices called
funnel-stops available for some objectives. These fit into the rear opening of the objective in order to do an aperture reduction for darkfield). I tried my simple "mask" on other objectives and did not get the desired effect, just some vignetting. It seemed to depend on the optical design of the objective, and whether or not an aperture placed at the rear is close enough to what would be (optically...
I'll let Rik sketch it out
) the appropriate location for a diaphragm.
My take was this...
With a compound microscope I was adding typically another 1.67-2.5X magnification by using the projection eyepiece needed to place the image on the sensor. With the relatively low NA on the Nikon universal objectives; and because of the high magnifications of my modern high NA objectives with the built in aperture (40X and 100X) I was already, even with the apertures fully open, in the realm where I was losing more resolution to diffraction than I would like. Additional stopping down, even slightly, caused a noticeable loss in the resolution I was getting. With my 20/0.70 I actually had a little "room" to play with. I could stop down a little before the resolution really crashed from diffraction. If I looked closely I could see some loss, but the benefit in the appearance of the darkfield image made the trade-off worthwhile.
My hunch is that with something like a 10/0.30 or (even a 10/0.25) used directly on bellows (with no addition magnificatioon added) there may be times when -- if you can get the aperture in the proper location-- a slight stopping down would result in an acceptable trade-off between DOF and resolution. (Roughly the "effective aperture" of a 10/0.30, at 10X on bellows is f16.7, and a 10/0.25 is f20. So you can see that there may be a small amount of room to make such a compromise).
(edit.. John, right after I posted this message I moved on and saw your post in the image gallery section where you already suggest exactly what I posted below... I think a vaguely remember someone trying something like this with a lens that had an aperture. Might have been lauriek, or you! Definitely worth exploring, so I'll leave it here as well so hopefully more eyes will see, and maybe experiment, with it)
Even if you did not want to take the resolution hit I could see a possible use. Imagine a stack like your ladybug. You don't want to lose anything across the face, but as you get to the back it would be nice to have a more "natural" fall-off in focus (instead of the dramatic and unnatural fall-off you sometimes get if you stop running the stack to the back). It seems it should be possible to run the section you want sharpest at full aperture and then gradually stop down and run larger steps as you get to the rear. A bit complicated but it's an interesting thought.