Why not just convert all of your spending for the next 3 months onto that card, if you are not spending more than 1k a month then buy some gift cards and use them later...
also if you are not spending 1k a month then the AF for this card is not going to be worth it after the first year and you should probably look at the no AF version
Don't dismiss the gift card idea too quickly. It doesn't have to be gift cards to a specific merchant. Get a visa gift card. As stated above, then use the visa gift card for your spending in place of your CSP. You're just time-shifting your spend.
There are lots of ways to liquidate gift cards as well, but you're going to have to go read through the travel blogs and flyertalk for all that.
Chase is pretty good about treating most things like a purchase instead of a cash advance. I paid my rent using a credit card and even though it's categorized as "Finance/Other" it counted toward the minimum spend on my Chase Ink Bold. Citi on the other hand is different, I believe any charges that come from a financial institution (such as a rent/mortgage payment processing firm) are treated as a cash advance. I think it's b.s., but it is what it is.
To be safe, you can call up your credit card providers and request to have your cash advance limit reduced to $0 so you don't inadvertently make any cash advance transactions. Just make sure you pay your bills a little bit earlier when you're experimenting in case the charge doesn't go through and you have to pay through some other means.