Well first the CallerID is from the person calling and therefore part of the INVITE. A 180/183 is a REPLY from the PBX, the PBX would not be sending back CallerID in a reply because that's really not how it works. Yes, it is possible but that's not how Asterisk works.
So Caller Phone is going to send it's CallerID to the CME which should pass that through to FreePBX, when FreePBX sends the 18X message back, there's no CallerID in those messages. It will pass the CallerID to the final destination.
You have to look at what the CME is doing, because it is in the way and well Cisco is known for doing things their own way and not standard.
But there is no callerid in replies only in requests.