I did get a new router (Hitron CGN3ACSMR), so that was an upgrade from the old Hitron CGN2, the swiss-cheese one, lol.
However, there is one more thing that I forgot to mention, and that may have been the root cause. With the old setup, I also had a Cisco Linksys E2500 N600 router, so I was running in bridge mode.
Now, with the new router, I left it in gateway (tried running it in bridge, but my E2500 was for some reason cutting down my download speeds to about 25-30 Mbps, instead of 120-130 Mbps that I get with CGN3 in gateway).
With regards to WiFi coverage, in both cases, my Mac was only about 3m away from Apple TV (and the router), so that shouldn't have been an issue. But that old bridged setup may have been the cause of choppy AirPlay playback, probably because of E2500 acting up.
Anyway, long story short, I'm good now. Taking E2500 out of the equation is what most likely fixed the choppy playback, and probably nothing to do with increased speed and bandwidth.
Last edited by DonR; 2016-08-27 at 01:18 PM.
Reason: Changed to correct terminology (Mbps, not MBps)