Im having a similar issue in my 2011 mkx. It doesnt do it every time and its sporadic. When mine acts up it also kills my climate control. Any ideas? 

I had this same issue. It turns out it was the touch panel. I took it to a dealership and it only costed $200 to have them fix it. Mine unfortunately started turning my stereo on in the middle of the night and i would go out to a dead battery. 

Isn't the valve supposed to open after filling up? Maybe it’s not doing so (and failed in that way). I know usually they stick to a semi-open position but this case may be different.   You can either see if you can test its actions by connecting whatever voltage controls it (I didn't look it up). And see if it opens-closes correctly. If it doesn't thats your problem. If it does, then check the output of the connector that controls it on the engine, make sure its outputting correctly.   3 years @ 36k is crazy btw. I go 18-20k a year 😅. Lots of idle-time as well - but for the last 3 years I have replaced the purge valve in October or November every year just as it got cold here in New York. Its a different evap code each time too.

2018 Edge Titanium 3.5L AWD

Correct, no codes.   Air filter is clean - changed only 4K miles back. Spark plugs and PCV valve changed 2K miles back.   I'd not suspect any of those considering idle stumble occurs only immediately after gassing up at idle, and then nothing until the next time I gas up.   Exact same symptoms which cleared with a new EVAP valve - just wish I knew the procedure to test the valve, but now leaning towards spending the $70 for a new OEM replacement.            

No codes? Besides evap, did you check for a dirty air filter? Any possibility one or more injectors dirty? How many miles on spark plugs? Plug boots in good condition? 

The rear drive does disengage on my 2017 Sport and I'd be very surprised if it's changed on the later models.   Please add your Model/Year to your profile signature - https://www.fordedgeforum.com/settings/signature/    

Pretty sure my rear axle doesn't disengage at cruise speeds. That feature was added to 2020 and later AWD models.   Starting tomorrow I'll be rotating my tires twice a year with each oil change.    

Some months back, I ran over something which destroyed my rear driver tire.  I only had about 17,000 miles on the original tires.  I had the service writer confirm with the shop that I only needed one tire.  I was relieved.  I have my tires rotated twice a year with the oil change.

36K miles and three years after replacing the EVAP valve its stumbling at idle immediately after gassing up, and NO I don't click the nozzle again after it shuts off.   No codes this time and I removed the valve and without power its shut and holds vacuum.   Might buy just the valve and attempt to install it on the original assembly.