when you change your dates the rates changes ... that is always the case, no idea what kind of 'rate stays the same' experience you have with the old Hilton webpage. Sometimes you can cut deals with the hotel directly, like split up a GLON and get 2 room ....
Arriving a day later should not be problem, as long as you pay for the first night. I was a pre-pay reservation and had a misconnect in MSP; called up the hotel and asked them to check me in anyway and I would show up next morning ... was no problem at all.