Just to check, do you get the hum if you just touch a cable from one jack to the other? That is, if you connect just the ground from one module to the ground from the other?
And it’s only with modules on two different PSUs, right? Any two PSUs?
With no modules plugged in, is there a direct connection between the grounds of the PSUs? If you check continuity between the center pins of one of the 16 pin headers on one PSU and those of a header on another, is it there?
Does the hum change if after plugging in the cable between two modules, you move it around, twist it, etc? Does it depend on the length of the cable?
One other thing to consider trying is building a Faraday cage around the transformer and mains input.
Added: If it is the case that you get the hum if one module is plugged into PSU1 and the other into PSU2, but not if both are plugged into PSU1 or both are plugged into PSU2, then one possible culprit is the part of the loop formed by the long-ish leads you have running from the transformer to the PSUs. You might try having these leads branch out close to the PSUs instead of at the transformer — maybe just run 2 wires from the transformer to one PSU, then 2 wires from there to the next PSU, then 2 wires from there to the third. (Like this.) Or it might work to keep the separate wires from each PSU to the transformer but put them parallel and close to one another. You might also consider putting the PSUs closer to each other. The point being to minimize the area between the ground wires between one PSU and another. You can try running the 12VAC wire far away or not and see if that matters. My guess is it won’t matter much once you’ve minimized that loop but I could be wrong. Getting rid of hum basically involves trying every (safe) thing you can think of, whether you understand what good it’ll do or not, until it goes away.