"He just wants to know that you love him the same as the others but he can't say that."
I think you've got overly focused on punishment, discipline and your DSS learning to toe the line and see your point of view.
I think you've forgotten that he's a teenager, who feels isolated in his own home and family. Whether or not it's true, he feels like that, and needs the adults in his life to help him feel included.
Whatever your motivation or interpretation of Christmas. What happened was that you enabled your son to exclude DSS at Christmas. You say you did it as it was Christmas - a special occasion. But seen from DSS perspective, you showed him that on a special occasion, he was pushed away. On an occasion like Christmas, which is supposed to be about family and togetherness. Sounds pretty upsetting to me.
And giving him some money to make up for pushing him out of his own family. Ouch! His step father excludes him, then pays him to spend more time out of the family unit.
I wonder if your reaction being all about how DSS should behave, instead of empathising with a teenager who is feeling isolated and pushed out, well, this is the way rifts start.
And denting his right to feel that way is giving him the message that others can exclude him and he has to suck it up and not show he's upset.
I don't think he's 'milking' it which you've said a few times about both situations.
I still can't fathom why your son deciding he didn't want to share a room with DSS at Christmas time resulted in you agreeing (& your wife agreeing by default), and telling DSS he must go to a room away from the rest of the family.
Why did you agree that DS was allowed to object/ dislike/ push out DSS? Why didn't you move DS and let DSS stay? Why was DS allowed to behave like this and get his own way, whilst DSS gets the consequences?
You may feel DSS is wrong about his place in the family. But trying to push him into line and deny his feelings will only increase his isolation and upset.
I'd suggest responding to your step sons feelings, rather than focusing on his behaviour in isolation.
Remember he's not fully grown yet. So even if you can remain polite and warm in a situation where you feel you are being excluded and isolated... A teenager probably cannot.
It's good he's telling you how he feels, it shows he thinks you might care.
Good luck.