You’re more than likely correct that the pooping is a crating issue, but mention it anyway. The vet needs to know the whole picture to accurately diagnose - even if the whole picture is information that turns out to be not related.
If they vet finds nothing medically wrong with your pup - I second (or third?) Elenfair’s suggestion of asking for a referral for a behaviorist. I also recommend (and IIRC correctly did so in the last thread as well) the tether training that Calliope suggested above.
Good luck!
Oh, and as a volunteer with a rescue group, may I just commend your patience and willingness to work with this issue. So many would have just returned the dog after a week. It’s nice to know that there are still some people that understand the commitment they make when getting a pet.