Did your term set creation work without error? (from your last post)
Termset creation must happen before you can add record types to the default integration settings.
Make sure the record types you wish to use have the checkbox ticked to allow them to be used as a sharepoint list item (see attached)
I figured it out the issues with multiple Managed Metadata Service Applications. I could not find a fix but all I did was use a different Managed Metadata service application. The service account which I was using probably had enough rights on this service application and it started working. Also I changed the service connection in SharePoint to use this service application only.
Hopefully it helps someone else.