When I’m down to the last shot in my current pack of film, I want to cut out a 35mm strip of it, then put it in my Canon A-1 (in a darkroom, of course). And use the chemicals, which I assume are in the pouch at the bottom, to develop it. Is this possible? Any advice?
1) the film holding shebang (cassette, the resp. essential parts of the camera) will not allow to bring the sheet film into the focal plain.
You realized that. To circumvent this a relay optic has to be used.
I just trimmed an old instax print and stuck it in the back of my SRT. I imagine after making the exposure, you would then take it into the darkroom, and with a piece of plastic (old credit card) drag it from the chemical pod, along the image area. Try it and see... I bet it would work. Let us know how it goes!
My first critical question to answer before going too far on a plan like this would be: Can you even safely trim unexposed instax film down to another size in a way that allows it to properly develop after exposure?
It has been a long time since I really played with instant film, but it seems like trimming it pre-exposure is going to at least give you problematic edges to the image.
If it's the mini film (size of business card), I think each film sheet can be removed intact from the connecting-paper. So, cutting is just done to simple paper, not to actual film emulsion or chemical pod.
Unlikely that you're going to be able to get it to work in a useful way, even if the piece that you cut out doesn't fall apart entirely. The "film" is designed as an integrated unit, with the small amount of chemical housed in the pod spreading from it in a controlled way only if the whole thing is intact. The data sheet for Instax Mini film includes a cross-sectional diagram of the film before and after development, showing just how complex the structure is.