Shangri-La would be my choice for what you are looking for and you should be able to stay well within your budget for a horizon club room in the river view tower. Just call and ask if they are selling rooms for your dates, they don’t have the best websites.

I think 12 on Hengshan is great for huge bathrooms/tubs plus a superb location, but alas it has no river view. Same issue with Capella which is a great setup in old traditional lane houses. WA and Pen would be my other recommendations.