Consider calling the hotel directly and asking if you can use the government rates.

Some hotels have a state rate because there is a separate state per diem.

In my experience, Canadian and UK military folks check in with government rates here in the US regularly. I believe Canada just used the US per diem rates. For car rentals, the Canadian military historically has been included in the USG rental contract. There is no master contract with hotels, however.

Of course, I'd still call first if I was really concerned.