Not specifically with Hilton, but in general multiple AMEX offers stack with each other (and with annual credit rebates etc.). Personal experience with DL and Marriott.

IMO the 20% by itself is sufficient inducement and if you get the extra $150 then so much the better

If you're asking about the "charge to the room" aspect, there also IME AMEX looks at the total amount charged to the card and does not distinguish between base rate, taxes, and room charges.