Just an update in case anyone else is having the same problem.
Called support. It looks like the problem is that the DHCP server (on the existing LAN) and the Almond+'s built-in DHCP server were fighting each other. They told me how to fix it:
1) Connect the WAN port of your Almond+ to your existing LAN switch with a cable
2) Unplug your Mac/PC from your LAN and instead plug it directly into your Almond+ via one of the Almond+'s LAN ports.
3) From the Mac/PC, enter 10.10.10.254 in your browser; enter the Almond+'s admin uname/pwd.
4) You then should be able to proceed with the instructions in the thread above (updating the firmware, hard reset, etc)
5) Unplug the network cables from the Almond+
6) Reconnect your Mac/PC to your existing LAN.
Hope this helps someone.
.../john