Get a laptop, write a script to randomly enable/disable wi-fi every $timeinterval (and log whether or not it was enabled). (Also need to block the taskbar icon, somehow... can probably just hide it.)
If 10 minutes of Wi-Fi being on is enough to cause noticeable symptoms, it should be quite easy to prove that - if you can successfully determine whether or not Wi-Fi is on, better than chance, you have one heck of a significant result! You could save lots of people, most likely, from nasty symptoms
And if not... well, you have options there too.
(Of course, you have to make sure you get enough trials- and fix it ahead of time, can't just stop when you see a significant result!)