"If anything, cancer resistance (which would probably mean less cell mutation ability) would be disadvantageous from an evolution standpoint because you would have less variation and consequently may have trouble adapting."
Evolution doesn't work that way. It doesn't favor mutation because mutation is "good" for evolution. You have to look at it from individual genes, and there the story is just the opposite.
Evolution happens in spite of, not because of genetic predisposition to mutation, because it's vastly more likely for a mutation to be pointless or harmful than beneficial. If you have a gene that makes mutation in the genepool overall less likely, that gene will be more successful at spreading itself, because the mutants have, on the whole, far less chance of success than the originals (which have already proven their worth in a long chain of ancestor individuals carrying them). Of course every so often a mutant gets lucky and is more successful (or at least not less successful) than the original -- this is what selection is all about -- but statistics are against them.
To elaborate your scenario: suppose the environment changed very rapidly, and adaptation in some direction were necessary to survive it. If by some stroke of luck a gene that increased the mutation rate happened to be there at that moment, defying the odds, it would find a favorable environment, but only for as long as the rapid change is required. Generalizing this: a successful genepool is one where the mutation rate is "just right" for adapting to the environment. Too much mutation and the genepool isn't stable and will eliminate itself, too little mutation and the genepool will be eliminated by the environment. In this balance, the odds are stacked in favor of avoiding mutation.
And all this is orthogonal to the discussion of how cancer (the uncontrolled reproduction of cells) is related to the capacity for mutations (infidelity in the copying process). Cancer resistance and mutation resistance are related, but by no means the same thing. To borrow a computer image: your computer has copy processes with very high fidelity (only the occasional alpha particle to spoil the fun) but this doesn't protect it against worms, which copy themselves unwantedly but with the same high fidelity. This analogy is badly flawed in obvious ways (regular programs are not designed to copy themselves, cells are), but I hope it gets the point across.