As the prices of items and services go up, a lot of retailers (automobile dealers, sellers of real estate) either don't take credit cards or, as in the case of dealers aligned with Amex's car buying program, take them only for a portion of the selling price. The amount the OP is spending here falls below those thresholds, but along with the OP, I would have been surprised that his contractors would take credit cards, as I and many of my friends have dealt with tons of contractors over the years who would not. And I agree with the suggestions made that any contractor who is accepting credit cards might very well negotiate a lower price if straight cash is paid.

Since this is FT and questions of saving money may be relegated to the desire to earn miles and if the OP decides against negotiating the price, perhaps his best option is the Starwood Amex. With the spending he's outlined, he should get the 25,000 bonus Starpoints currently offered (10,000 at first purchase, 15,000 more with $15k spending, which seems to be his remaining budget after spending the initial $3K on the Chase card) plus he would earn at least 15,000 more Starpoints based on his spending. Even if he does not want to use these points at SPG properties, that's 40,000 Starpoints which, with the 5000 point bonus for 20,000 point transfers, would convert to 50,000 airline miles on Delta or US Airways (which could then be used for Star Alliance flights).