The UNO responds in a way that isn't erratic as noise causes, it literally follows it's own logic, or gets screwed up and follows bits and pieces of my logic that I've written. Outputs aren't just fluttered or flashed, or held stuck open, they follow actual routines.
Yes that is noise induced erratic behavior. What happens is that, say a register, probably the program counter, gets a corrupt value in it and that sends the code off executing from some other place in the program. When a processor goes wrong it goes wrong in a big way not just fluttering outputs.
but I've isolated the power sources as far as I physically could
Maybe it is not enough?
I've purchased another UNO that I will try Monday
It could be you have a faulty processor, but I still think it is a interference problem. What about the case? Is that grounded to a solid mains ground?
What you are seeing is not usual but it is not unique either.
However, as far as I can see, the "reset" and I use this term loosely is no way by that I can see caused by a ripple in the dc supply.
Often this can be difficult to actually see. You need a good storage scope to catch the impulses. Have you probed round the rest of the circuit to make sure the waveforms are as you expect them to be?
There is only a limited number of things I can suggest remotely, it might be time to get a good consultant in to actually examine your system.