What I've usually seen with canonicals is that Google either removes the noncanonical page from its index, or it ignores your canonical and treats them as two separate pages. I haven't seen an example where a canonical lets you get the best of both worlds.
I agree with Nozzle - you can tweak your existing content to target both phrases! Google understands synonyms, so if anything, you're just creating a more all around relevant page.
Good luck!
Kristina