Yes, Asterisk can’t bind to two ports.
You could do this with OpenSIPS.
Why don’t you just let the internal clients register on the alternate port? Would that not solve all of your issues?
The only other thing I can think of would be a bi-directional full cone NAT in a Cisco or other high end router. If you mapped port 6622 to 22 on the inside with a reverse policy the RTP invites would still be correct in the SDP messages and the change would be invisible to Asterisk since it is still writing to port 22. The dport doesn’t matter as the network will take care of that.