It makes me wonder why these boxes are missing their covers in the first place.
You say you are in Chicago, the land of EMT, this whole system needs to be closed to prevent the spread of fire.
Is there a problem with box-fill that covers can't be fitted?
Either way, I have a problem with covering any sort of junction box with insulation.
Maybe Greg or someone closer to you, could give some direction on this.
I note in your profile you are a teacher, is that in Electrical Tutor?
Please note that we don't field questions of the DIY nature here, if you don't hold electrical qualifications, please seek the services of someone that does.