Adwords: keywords apply to all Ad Groups!

Hi,
My client sells products online. These products do roughly the same thing as each other with a slight difference to each other. Heres the rub: that thing that differentiates them is something that noone is searching for. Ive done lots of keyword analysis and noone searches for the differing factor - they do in isolution, but not: differing factor + client product.

It sounds like they should just be in one Ad Group doesnt it? However, because of the different destination URLs (each product is on its own page), this is not possible. I dont think its a good idea having duplicate keywords in different Ad Groups (unless anyone here thinks otherwise).

Im going in circles with this. Ild appreciate any suggestions/advice.