Begin with Barclays Arrival to earn your $400 + 10% return on your first stay (I guess the plural would not be applicable here).

Then move in with Amex Plat Mercedes Benz that does give you 50K MR points plus valuable additional perks. I agree with Dave that I've never seen FHR rates go lower than what you can get otherwise, and that's for any hotel not just FS, but the perks are great. You can also book your hotels directly with the MR points, but the rates will be lousy. If you don't care about transferring the points into an airline program, just cash them out via a gift card of your choice to offset the annual fee.

Then I would switch to Chase Ultimate Rewards program by applying for CSP, and its business cousins Ink Bold Plus and Cash. You can use UR points to book your hotels directly or just cash them out to offset the costs.

Pay for your stay with Chase cards as others suggested. Hotels normally don't care how you pay at the end of your stay.

Most folks here will tell you that using MR and UR points in this fashion is a crime against humanity, but the important thing is to do what works for you, not for anyone else.

Play your cards right, and you get at least $1,400 cashback for your trouble in sign up bonuses, even before any cashback.