-- Last Updated: Sep-26-12 7:51 PM EST --
Here's another idea, and this one is guaranteed to help enormously.
Someone mentioned using straps threaded through the car itself to hold the boat down. Go ahead and do that and then take it one step further with two more straps. Route one strap so that it loops around the canoe and back under it, returning to the original side, and loop that part of the strap around a door pillar. Do the same with the other strap, looped around the door pillar on the other side. Take up the slack in these two straps so they oppose each other tightly, and the result will be that the part of the canoe wrapped by them will not be able to move side to side at all.
If your end tie-downs (and/or near-end tie-downs, as described above) have effective "angles of pull", they will at least minimize side-to-side motion of each end, limiting how much the canoe can pivot around the point of the two door-pillar straps, and as described above, your opposing set of front and rear tie-downs will completely eliminate forward-backward movement. The boat will be pretty solid if you can do all this.
This will be quite a jury-rigged-looking setup, but without a proper roof rack, you'd best do what you've gotta do to keep the boat secure.