TL;DR - you should have zero issues leaving your middle name off your tickets
I'm really surprised they let you set up GE with a different name than your passport, but that should give you a clue how little they care about middle name.
I have a middle name on my passport and my Nexus/GE card, but I never, absolutely never, put my middle name on any plane tickets. The same for my husband, we never put his middle name on tickets, even though he doesn't even respond to his first name, he goes by his middle name in daily conversation. Even when I book tickets for my dad, brother and nephew, who all have the exact same first and last names, I don't put middle names on the tickets.
We've never had a problem at a GE kiosk, even on carriers that do not have our known traveler numbers, or on last-minute irrops where we ended up on a different plane going to a different entry airport (e.g. NYC instead of ORD) than we were originally ticketed, etc. If the passport number is registered as GE and the fingerprints match, you're good to go, as far as I can tell. <shrug>
I know I took my niece on an international trip last summer and there was a typo in her last name on the ticket that no one at the airlines or TSA ever caught, and I don't recall any problems using global entry kiosks coming back into the country. She also didn't have a middle name on her ticket, because I booked it.
To me, having the middle name on an air ticket is just one more thing to go wrong - there's no error if it's not there, but if it is there, it's one more thing that could go wrong. Leave it off. The only people who I would recommend having a middle name on a plane ticket is if you need it for 'redress' purposes - like a suspected terrorist has your same first and last name or similar, and you keep getting sent to SSSS screening. Or if it's a young child that goes by their middle name and won't recognize and respond to their first name, then a middle name is probably a good idea.