Ah ha! Double post, but worth the bump.
You can reset your EA account using a linked account, such as an XBL tag. I did that, and got this:
I just wish I could login using my XBL account rather than the Origin one :(
Edit: YES! FUCKING AWESOME! Sort of.
For those following, it looks like the link to my XBL account still worked, so I was able to download the EA Sports "app" on the 360 and log into it to suss out some info:
The fucking thing won't let me change the email ("Unable to update your account info at this time") but at least I can see the email they used. I can't see the account name though, I don't think. But it's a start!