Seeing both shows is something we do on a regular basis.
Its pretty sure that any "secret plan" that ONE Disney fan thinks up has probably been tried by hundreds of other "insiders" to maximize the experience.
Disney seems to actually HELP with these schemes... for YEARS it was impossible to WALK the (relatively) short distance between MGM and EPCOT... even after Boardwalk opened, the pathway had a locked gate under one of the traffic bridges to deter any foot-traffic between these areas.
Then one year as we rode the boat to MGM, we took special note that new path-lighting had apparently been installed and the gate was now opened!
We watched the night show at MGM and, with about 45 minutes before IllumiNations show-time, we decided to attempt to "hoof it" to EPCOT to catch THAT show.
We didn't dawdle, and actually had enough time to pause at Boardwalk, sit for a few minutes and sip a cappuccino, then stroll across the footbridge and thru the Int'l. Gateway and up to the bridge near France in time for the "Five Minutes" IllumiNations announcement.
BIG TIP: Just before you go to WDW, set everyone's WATCHES accurately TO THE SECOND using an "Atomic" clock (any clock, on the web or otherwise, based on WWV "U.S. Bureau of Standards" time.)
WDW major show start-times are almost always EXACTLY ON TIME.
I have amazed people by counting down to the precise start of DISTANT Fireworks shows, just using my accurately-set watch-time.
(We can be peacefully seated in a rocker on the porch at Ft. Wilderness and I can countdown to the first explosion of "Wishes" across the lakes at MK (I had noted the EXACT time of the first "bang" on our first evening) and every night it was on-time... gives YOU a real aura of POWER to the "tourists" in the vicinity!