Hi Jim,
Apologies if I don't understand your first question correctly, but there are no specific permissions set within the DBXL Admin tool. Access to the forms is controlled using standard SharePoint server ACLs with each project having it's own subsite and then form libraries within each subsite. Yes, the issue appears to be solely with new users into the organisation whose account is created within the NEW domain who didn't have a corresponding physical account in the OLD domain where the SharePoint farm currently resides.
The account that the system uses on the OLD domain has a mirror account on the NEW domain, but we don't have any kind of AD permissions to be able to work with groups or user accounts on the NEW domain, as it's a managed service now and we are currently running v2.7 of the tool.
Can't understand how a single group controls access to both the READ and WRITE groups and all users seem to be okay with using the web services to read data, but not to submit back.
I am considering migrating the whole SharePoint farm onto the NEW domain in the hope that it will solve the issue, as it is growing over time with more new users joining the service.