I'm afraid it'll have to be a new H1 because when you switched to EAD, you stopped working on H1 and it expired anyway.
There was still time to go back before expiration if you worked for the same company - they could've just switched the I-9 back to the old one saying h1, but it's too late now I think.
As to the H1 cap, I don't know if it's been reached yet. If yes, you're out of luck.