Why tax it, put the $4,000 into an IRA.
The idea works, but what you are talking about is about the equivalent to make a 180 on the LSAT. It is possible, but I seriously doubt you can consistently get that type of return.
I can't argue that cc arbitrage has $0 return, because it obviously can have nominal results. However, your time would be better spent researching mutual funds for an IRA and saving your money.
You'd make more money if you just bought real estate. You would get a huge deduction off your income and depending on the market see a larger return over time. Even more if it were able to lease at the rate of your monthly payment.