As far as I can tell, it is supported (conbee II being de hardware and deconz the software, https://github.com/dresden-elektronik/deconz-rest-plugin/wiki/Supported-Devices )
As for the difference, I find the conbee II + deconz combination to be a tiny bit more stable and user friendlier compare to cc2531 + zigbee2mqtt. Deconz is available as add-on for HA with platinum integration status. 
Zigbee2mqtt has no UI and requires a bit of coding experience, knowhow of flashing (newer) roms to the device and requires two other components in order to do so. A CCDebugger and a Downloader cable compatible with cc2531. As where conbee gets their firmware upgrades just by going into the gui and press the update firmware button.
I was doubting myself too and got both at some point to give both a good spin off. I sticked with conbee with deconz, just because its easier.
Zigbee2mqtt supports more devices though, so if the list is all the devices you currently own, then both will be fine. If you plan to expand, check the lists for both and see what is compatible. I’ve learned deconz supports more than what is listed on the github page i referred you to, tech guys are not always the best in doing administration tasks as well xD
Last thing to consider, zigbee2mqtt is open source, deconz is not. So with zigbee2mqtt you could script to add new compatibility. Deconz is fairly easy to ask the devs and some contributors to write the compatibility for you through a request on their github page.
As for stability, both will do just fine. Get yourself a usb extension cord (small one will be fine of 0,5 meters). Both sticks are known to have issues on some systems when plugged directly into the USB port.
Then when I read about you not having enough coverage, that would mean you have an unstable zigbee mesh network. A large network requires some zigbee routers in your network to expand the range. A zigbee device plugged directly into a power source (can) act as a router. A zigbee lightbulb for example acts as a router where wireless devices can connect to to expand the range. If you only own one gateway ( xiaomi, cc2531 or conbee) And devices are not acting as a router, you could add an extra cc2531 or conbee stick to your network on the ground floor and tell them to act as routers.