Thanks for all the advice! It is a throw over both hips, for us, but we just call it koshinage. I'm not too sure but different variations might have different names. In response to an earlier post the gradual step up to koshinage as you described is something we practice; I just never quite get the earlier parts right so the full throw never works out! Most of what you said was familiar, but the idea of keeping your legs stiff was a new one for me. If I'd kept my legs more stiff they wouldn't have cracked into the ground like a whip, I bet. (though my foot's feeling much better today!)
The best thing I think my sensei teaches on that breakfall is to let your weight fall past nage's hips so that your're much closer to the ground before you rotate for the breakfall. If only I could get that far without panicking!
As far as being tall, it hasn't really hurt me that much; shihonages are hard to get low enough to go under the arm and I've yet to pull of a decent Koshinage as nage, not to mention getting bent over all the time on shorter ukes. But hey, there are plenty of large, very good aikidoka out there, so I guess I shouldn't complain.
Thanks everyone for the advice! It is much appreciated!