Hi,
Thank you for detailing the call flow for me.
Yes, the scenario is not too straight-forward, but I've seen something similar before, usually, with Cisco gateways or CMs.
The 3.a is not an error, it is a valid re-invite,
This issue started looking like a support case, and slightly goes beyond the forum's purposes : -), but let's make a step forward to see if we can sort it out.
The errors you showed complain on a call state mismatch rather than on unknown PT. Please open RtfConfigXxx.xml file, enable all labels on Global Call, Global Call IP, gc_h3r and "Debug" in SIP stack sections, re-enable the rtf config (or restart HMP), and repeat the call. Then zip up the fresh RTF log and attach it here (it won't be too large in compressed form). Please make sure that the log contains the very beginning of the call and all SIP messages are in it.