Changing the cck field back to user in tables _cck_store_item_users and _cck_core seems to solve the problem. I'm thinking of just writing a script that updates these fields after each save as a temporary solution.
You can't have multiple forms saving to the same tables. What you can do is to use restriction plugins from ACL pack to restrict fields for user that is not in some user group. E:g. if you have fields a,b,c,d you can put admin group restriction on e.g. c and d - this way only admins will see all four fields and normal user will get only a and b fields.