OK, so it's been a while but we finally got there! I raised a track with TS (and I believe Riz from TS in the UK might have spoken to you @gwootton?). Turns out the problem was that rather than being an Environment Manager dashboard issue, it was the agent on one of the servers which wasn't collecting any native server stats (CPU, memory network, file mounts, etc). In the end, we removed the server platform from EV, stopped the agent on the server itself, removed the data directory and restarted the agent. This added the server platform back in and, lo and behold, all the resources are populating as they should.
And I was able to add my metric viewer in the EV dashboard.