How large are the specimens and are you shooting close-up details of them or the entire subject, or both? Will all the shots be taken on the copy stand or would some be done at a greater distance? How are the resulting images being used?
What I'm getting at is how much magnification you need. For purposes of macro photography, magnification is expressed in relation to the size of the image sensor area in the camera (formerly the size of the image on the roll of film, of course). So with 5DII an area approx. 24x36mm or 1x1.5" is equal to 1:1 or "Life Size" magnification. Of course, it might be much larger than that in it's finished form, as a displayed print or image file posted on the Internet.
5DII is about the best Canon camera for the purpose, with the greatest amount of fine detail. (1Ds MkIII is the same resolution, some other manufacturer's cameras are higher resolution, but might lack other features).
The lens you choose is another matter. It might be several lenses, for different degrees of magnification or for other reasons. With macro lenses you also have to consider working distance... which might be limited by the "copymate" stand you are using. I'm not familiar with that particular model, but have used similar stands in the past.
Usually on a copy stand you are limited to shorter macro lenses, probably a 50mm or similar most often. A 90mm or 100mm would generally require you to move too far away from the subject, when working on a copy stand. It might not be any problem, though, if using the camera and lens on a tripod or handheld.
Canon has 50mm, 100mm and 180mm macro lenses for use on 5DII.
Also the MP-E 65mm is a specialty macro lens for higher than 1:1 magnification. It's manual focus and goes up to 5:1 mag.
Two Canon Tilt Shift lenses are also often used for macro or near macro work... TS-E 45mm and 90mm.
Almost any lens can be used for macro or near macro work, with the addition of some macro extension tubes. These increase the lens' close-focusing ability and level of magnification with it. However, it sounds as if distortion might be a problem, so a "flat field" lens design would likely be best. That eliminates a lot of non-macro lenses from consideration.
Please tell us more what distortions you are seeing, that are a problem. If it's soft focus in some areas, well when shooting macro or close-ups depth of field can be real issue. This can be offset to some degree by using a smaller lens aperture... But there is a limit to that, too. One is having adequate light to use a small aperture. Often with macro photography, you can spend an hour or two setting up the lighting, and just a few minutes taking the photos.
With small apertrures there is also an optical phenomenon with digital cameras called diffraction, where with really small apertures you start to lose fine detail. There are some ways around these things, such as using special software to do "focus stacking" of multiple shots.
Has your museum considered it might be a lot more cost effective to simply hire a professional photographer who already has all this gear and full knowledge how to use it? There is a great deal more to macro photography than a copy stand, lens and camera.