My impression is 6~8cm of rack-and-pinion travel is typical. I measured 7cm of travel for the microscope next to me. I can slide+clamp its head another 17cm, up and down, from one end of the vertical carrier post to the other, before I have to move all the moveable parts – head, post, and the horizontal swing arm – up and down.
My father's solution to look at objects of wildly varied sizes was to mount a microscope head on a parallelogram, stand. [I will try to find a picture of one.] It allowed quick but coarse height adjustments. You might have to wait a little for the head to settle, especially at higher magnifications. He had a machinist fashion a carrier post. Perhaps an idea.