Don't forget you can use the SP card to reduce the cost of the paid fare by 1.25 cents per point if you can't find reward availability. If you're set on flying coach, you're unlikely to exceed 2-3cpm anyways, so by using Chase points in this way you'll save some money ($500 per SP card you get with the current bonus) and you'll earn miles on the flight as well since it's booked as a revenue ticket.

It's not free, but it could reduce a $1200 rt, for instance, to a much more palatable $700 and you'll also earn ~20k miles (so a roughly ~$200-400 return on investment if you'll be booking coach awards) on whatever alliance you fly--brings the effective cost down to $300-500.