Wow, interesting.
Usually, when we create a mapping between DBXL and SharePoint (with Object Model selected, and Publish Library and XSN checked), DBXL is able to automatically determine the name of the Document Type. The error:
No DocumentType found for ''
...suggests that DBXL fails to determine which document type the form (being submitted) belongs to.
I guess I would check the submit data connection in the XSN itself, but again, since it's submitting fine from DAT, this tells me the submit data connection is probably correct. I could check the form if you want - just attach it to this discussion via the Options tab.
Otherwise, I would suspect a network issue, where perhaps the DBXL and SharePoint - 80 app pools are not running under the same identity.
Keep us posted - if you need to escalate and/or set up a help session next week, email us via support at qdabra dot com.