You can get cash for your points at $0.01 per point. The $275 room probably did not include hotel tax which could be 13%+. It would be more like $300+.
So in your cases, either option will cost you about the same 29K which could be cash in for $290. Or pay $300 using your CSR and get 900 UR points which is worth $9 if you cash it in straight.
In theory you should be able to get the room on Chase UR site for $300 and use only about 20K points for it.