I had this exact issue. I went from participant to co-owner and got the "invalid card" error. I was frustrated after speaking to Goldman Sachs and Apple and hearing "everything looks fine" so I just messed around until I was able to fix the issue myself.
Here's what I did (among other things that didn't work)....
1. I went in to my Watch app and removed the old "participant" card info from it. I made sure none of the other devices associated with my Apple ID had any old card information on them as well.
2. I signed out of our family Apple ID (used for media and purchases) which has the co-owners Apple Card linked to it.
3. I signed out of iCloud entirely on my Apple ID.
After doing those three things, I went back into the Wallet app. When I tried to add a card, it directed me to sign in to iCloud with my Apple ID. Once I did that, the new Apple Card (along with all the cards that were previously in my wallet) were listed as options to add to my wallet and it allowed me to add them all. I did have to re-enter some card information for each non-Apple card (verify cvv and exp dates) and it directed me to the card issuers to verify, so it makes me think that signing entirely out of iCloud revoked all previous privileges. That may be the key as perhaps some old info is remaining on the backend and it just needs a clean slate.
Note - I had previously selected to sign out of iCloud and it still gave me the same error. But I don't think I was truly signed out for some reason. There should be a very noticeable difference with your phone when you are signed out entirely. All the info should disappear from your Wallet app, for one thing. So make sure when you open the Wallet app it looks like you are using it for the first time.