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One problem might be using too much of the microscope's exit pupil.
Microscope eyepieces for visual use are sometimes optimized to work with the human eye's pupil forming an aperture that only passes a smaller portion of the light exiting the eyepiece, which has an exit pupil larger than your eyeball's pupil so you can easily view without super-critically aligning your head in exactly the right position.
As your eyeball moves to different portions of the exit pupil, the image is focused at slightly different distances and with different distortions --- but, because you only see a small portion at a time, you see a nice sharp image. A point-and-shoot with a tiny sensor and lens entrance pupil sees the same. However, your DSLR has a great big lens entrance pupil, which captures more or all of the light from the 'scope's exit pupil at once --- overlaying simultaneous views of the image with different focal distances and distortions into a blurry mess.
To avoid this, you need to stop down as much as possible (and maybe use a wider lens) to get your DSLR's entrance pupil down to the size of your eye's or point-and-shoot's. It might be the case that you should just keep using the point-and-shoot that already gets decent results (solidly tripod mounted), since you may not be able to do much better with a fancy DSLR unless you also use a proper camera adapter.