Karl, it isn't just tying the two grounds together (you do need to do that). You also need to check the phasing. As others have pointed out, after tying the grounds together, put the meter between the center rail of one loop and the center rail of the other loop, it should read 0 or near 0. if it reads like 34v or whatever, the power supplies are out of phase.
I suspect that tying the grounds together will fix the problem, on a more modern power supply like the bricks you are using it is likely they are in phase IME. If they aren't, you will need to reverse the plug on one of them and make sure if you ever have to unplug it you know which way it is plugged in. If you can't reverse it (some plugs are polarized, one prong is wider than the other) you will have to grind down the prong to allow it to be reversed (you also can replace the plug with one with non polarized tabs).
