IMHO if you step-up to a 16-20 bore, shoot 7-7 1/2, and let the birds on a covey rise get out a little more, increasing the likelihood you have all the birds in the covey in the air when you shoot the first time, you will not double-up with late risers coming up into the pattern. That's about the only option at present you haven't considered. Normally, wild birds are not dallying around much, so giving them a little extra time should do the trick.