I would just glue some sort of "handle" to the elements. The "handle" could be a household suction cup like you mentioned, or something else non-metallic — perhaps a plastic spoon, for instance.
The type of glue you need to use depends on how much force you need to apply to remove the lens elements, and on what the lens elements are made of. Start with a milder, easier to remove adhesive, such as "glue dots" (the same stuff that they use to glue your new credit card to the paper letter when they mail it to you). Glue dots are better for use on plastic than rubber cement (which contains acetone).
Assuming the lens elements are glass and that they don't have special coatings, you could use cyanoacrylate (Superglue) to attach the "handle" to remove the glass. You can use acetone to remove the superglued "handle" from the glass. This would also work when reinstalling / repositioning the elements into the lens body, but word of caution: be careful when using acetone near plastic. Acetone can damage several types of plastic. Apply the acetone sparingly with cotton balls, swabs, and only to the glass. (Of course, when using any kind of volatile chemicals, use plenty of ventilation).