I know this is well after the fact from your original post, but this is something I have been struggling with for years, too. I believe I now have a working solution.
Like you, I set our iPads up initially in Apple Configurator, and apply a wifi profile, and prepare them to enrol in Meraki MDM. Every device that enrols in Meraki automatically gets the system manager app, but everything else is tied to a profile.
I have a grade level profile applied to each class's iPads. Originally I had embedded the wifi settings in each profile, and every year when I removed the profile (the quickest way to refresh/sign out of the apps), the wifi would disconnect after the apps were removed, necessitating a hands-on log in.
A couple of years ago, I had a brainwave that the wifi profile should be separate, and I created a wifi only profile, tied to a different tag that all classroom iPads get. This still did not work properly, and while a couple of iPads remained connected (for some reason?), the majority still lost wifi when the grade profile was removed.
FINALLY, I discovered that I had to remove the wifi embedded in the grade profile, and re-push the no-wifi grade profile - which of course meant re-connecting manually to the wifi again, BUT now it does work as expected! I am able to remove the grade profile, and the wifi stays because it is connected to another tag and is not included in the grade profile.
I'm a much happier iPad coordinator now!