I cant Commend upon your discrepancies in hardware and different HAOS installations, but i actually also just bought a HA-Green (a month ago), but it’s to early for me to make any opinions, beside it definitely consume less power(which was the main purpose, as it will have an isolated environment/Purpose), and in the end i will never end up with identical solutions, on this and my current Installation.
Other seems to have similar issues with ZHA, but first of all good “best practice” of Zigbee network, in a “modern” home, with various electronic Devices/Equipment is essentiall, below is a link from a community member whom dida good work in covering most issues there is to think about.
Feel Free to update this post if/when you more logs/info to add, like how many device Zigbees/repeater, but also location of the usb-dongle, compared to your Router/TV /NAS and HA-Server etc, also how large your WIFI-Network is, and Which Channel you Zigbees communicate on