I actually don't see that "cogito ergo sum" and Heidegger's "thrown-ness" are so contradictory. Descarte wanted to find a claim irrefutable by logic on which to found his subsequent thought. And he did. The fact he went on from there to separate mind and body in a way that Heidegger's thrownn-ness doesn't require doesn't mean the ideas aren't compatible.
The problem with Descarte's thought is not the first but second therefore: I think therefore I am therefore my mind is separate from my body.