You are certainly right, out of an abundance of caution (to avoid frying the boards!) I’m being extra-careful 🙂
Yes, I’m referring to ‘earth ground’, and now I understand that there shouldn’t be any expectation that either of the leads from the transformer would be equivalent to ‘earth ground’; it’s why some transformers have three pins and connect the *actual* earth ground to a third lead, used for safety ground and not logic ground.
To make things more fun, I’ve decided to power the Pi boards using the PoE ‘hat’ boards from Element14 (same as the ones from the Raspberry Pi Foundation), so the ‘other’ power supply doesn’t have an earth ground either; it is also fed from transformer taps, which pull power from the Ethernet cable. Since that technology is also designed to provide isolation, there’s no connection to an actual earth ground (or even a shared logic ground with the network switch) present.
I think this means I’m all good to proceed with the plan. Thanks for the helpful response!