Yup, all good strategies. AP power generally needs to be higher over any distance where the FSPL attenuates the signal. Higher SNR = higher rates, so if the goal is maximum throughput, the higher SNR is needed. If the mesh link is sufficiently close that mesh throughput maximums are attained at lower power, or if the throughput requirements aren't that high, then you can lower power. That's a design and requirements descision for sure.
Airmatch should follow the max/min set forth in the radio profile. If you change it after the current solution has been in place, you would either need to wait for the next solution, or force a new airmatch solution to be implemented (which would be run across all Aps on that MM). Or like you noted, you can force a specific channel/power with ap freeze.
Yes, if the distance is over 500m, you would need to set that distance in the maximum distance setting of that AP's 11a radio (which makes a good case as to why you would create a separate group for those APs so as not to impact the other APs that aren't doing mesh).