Regarding the leads to the display, I would suggest using ribbon cable to keep the leads close together. The ones used for floppies and older harddrives is half the spacing as the pin header. Cut a longer piece than you need and splice them a bit longer to spread them out and cut them to the proper length to fit the pin header. Try to keep them together as much as possible. If there's interference you could experiment with further grounding or isolating the display from the case.
The "newer" ATA133 cables has doubled the number of leads and every second wire is grounded. It's possible to implement this tactic with the 0.05" ribbon cables and 0.1" pin headers as well, but would probably be a bit messy (:
And yes, even with the display mounted in the original position there's some interference when updating the display. Not anything to worry abount unless you listen to a dummy load at full volume.
Daniel Ekman SA2KNG