It's either the pedal itself or the cables. When you tried the cables, were you able to route them away from the audio cables? A MIDI cable routed alongside an audio cable could cause noise to transmit from one to the other, unless they're very well shielded.
The ideal test would be to have another source of MIDI clock (like a computer), and connect it directly to one of the pedals (or, as direct as it can be, I know you would need the MIDI box.) Basically, isolate the MIDI clock from the rest of the pedalboard as much as possible, feeding it only to one pedal. If you do that and you still get MIDI noise, it's most likely the pedal itself.
Another possible test: with everything connected normally, turn on the pedal's loop, but pull the power plug from the pedal. If you still get noise, it's probably (but not 100% certain) that it's the wiring. If the noise goes away, it's most likely the pedal (also not 100% certain, though).