On the 2nd switch, I was able to at least get link lights on the front LAN ports after a factory reset. Setting the static IP on my client allowed me to get to the local device management page, so that's good.
Ended up carting both switches back to our build room and connecting them straight in to just a run-of-the-mill cable ISP connection, off of our corporate network. Got link lights, DHCP'd addresses, connected right up to the dashboard. Both switches pulled a firmware update and installed it before booting fully, but have behaved as expected afterwords.
All good now, thanks for the suggestions!