Thanks guys, those are great suggestions.

Where there is ethernet, it's all gigabit. I'm pretty certain that the amount of phone traffic on the network could be carried by the available bandwidth. These are not the most bandwidth-hungry users. Although we do have some security cameras on the same network that might take up a good chunk.

That UniData phone might be a good option for one or two of the users here who need to go all over the campus for certain tasks. I installed a Unifi system that covers about 90% of the place so it should be able to work almost anywhere.

This place has an even more patchwork electrical system than it does phones and network. I've tried powerline for a few single use cases in the past and had nothing but failure with it, unfortunately. I've used it in other sites with a lot of success, particularly with recent powerline devices, but not in this place!
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Matt