Very old posts here, but I'll add my two bits for people who come looking.
First--Are you sure you have the edible canna? Canna edulis/Canna indica. I guess I mean, what kind of yucky? Texture--fibrous, or just not what you are used to/were expecting? Taste--muddy/mineral(as the perfumers would say) bitter, bland, sour, turmeric or ginger-like flavors?
If you're getting unpleasant, ginger-like flavors, your canna species isn't quite right. They are indeed ginger relatives, as is the actual plant they make commercial arrowroot from, Maranta.
My mother boiled our roots--fairly certain they _are_ Canna edulis--for a good 45 minutes, with potatoes for comparison. I _think_ she peeled them first. They were bland, starchy, sporadically fibrous and a little watery (crisp, maybe?), but honestly I liked them better than cooked sunroot (Jerusalem artichoke). (Also no undo flatulence afterward. +.) Truly they are not just like potatoes--I've seen some people comparing them to taro--but I didn't find them offensive. I've also heard that there's pretty huge variability in stringiness between older and younger rhizomes.
She boiled them, hard. For _45 minutes_. I didn't think to taste their cooking
water.
I'm going to have a go at them tonight--cook them separately and add them to a venison stew--I'm doing stock from meaty bones my uncle's buddy's didn't want.