If you check out the Memory Alpha pages for TNG episode 'The Battle' and 'NCC-7100' it explains that NCC-7100 is the Constellation class model and it appeared in early episodes as simply a decoration for the ready room.
Later on they decide to make 'The Battle' and have Picard's old ship show up which was to be a refit Constitution-class just like NCC-1701-A, probably to save money on building and designing new props/sets. So for 'The Battle' (and three other episodes that were after it in production schedule) they replaced NCC-7100 with a Constitution class (my guess is this would have retconned out the NCC-7100 model as having existed).
For whatever reason they canned the idea of using a Constitution class model, but this must be at a point after they filmed the other episodes with a Constitution model in the ready room. The effects guy decided to use the NCC-7100 type and build a new proper filming model of the Stargazer. As a scene is already filmed where the ship's class is named they dub Constitution with the similar sounding Constellation. They then decide to put the NCC-7100 back into the ready room, where it can be retconned into being Stargazer, where it stays for the rest of the show.
In universe, I think you just have to pretend there's a Constellation class model whenever there's a Constitution class. Or maybe someone told him to blow up the damn ship and there was an accident.