I had similar issues whith multiples Wifi AP with same SSID. The HAA devices should use the better AP with the SSID configured, but with my test, it does'nt work well. I lose pings, and many HAA devices were in 'no response' in Home app. Other devices than HAA had not these problems, on same Wifi network.
For me, I solved my issue by having unique SSID on each AP and distribute devices on these AP. But that's a workaround, because if an Wifi AP fails, the devices will not connect to the running one, even if the signal strengh is enough.
So you could try to use different SSID on each AP you have to see if your issue is the same.