I'm wondering if anyone can solve this problem I have.

I want to move some living quarters (build new ones in new spot and remove old ones, in no particular order).

I can't remove the existing ones because my population is too high, and I can't build new ones because I'm at the 200 population capacity limit (ability to create new living quarters is disabled due to having 200+ capacity).

So is my only option to send off dwellers to a callous death to enable removing living quarters (I don't want to do this to the poor guys), or is there a better way?

Just a suggestion, if you can delete some other rooms, create more living quarters and then delete the ones that are somewhere else?

Once you've built enough living quarters to accommodate 200 dwellers you can't build any more, it simply states 'limit reached' when you open the construction menu. I'm in the same situation as dakranon, I want to reposition some of my barracks but as it stands I'll have to slaughter 40 of my dwellers in order to be able to demolish one barrack. Deep joy...

Sounds like it's time to send some dwellers to the wasteland.