Electrical Question: Can I pull wired, Old Work Electrical boxes through new drywall?

[Matt Greenfield]

My electrician insisted in rewiring my house without ripping out the existing drywall. In a lot of sections of the house this was a good thing because less drywall work, but there is one room that has old wood paneling that was severely warped. In this room, I would have preferred to rip out the existing paneling, and do the electric and new drywall at the same time. The electrician didn't want to do this because it would have caused more headaches with the inspector, so he says. Regardless, guy did a great job so not going to complain about order of operations, but I am in a bit of pickle. 

I have since done the demo work to remove the paneling and replace / add insulation and the new electric work is now hanging in place in "old work" electrical boxes. These are the boxes with the deployable wings that can be fixed into drywall, rather than needing to be nailed into a stud. I am now ready to hang drywall, but I'm not sure how to fit the already wired, electrical boxes through the drywall cutouts. I think the proper way is to "de-wire" the electric boxes, hang the drywall, pull the wires through the holes, reattach wires into the electric boxes and then push the rewired boxes into the hole from the outside in. This way the wider outside lip contacts the entirety of the drywall while the wings are being deployed and tightened in place.

Is there a way to pull the already wired, "old work" electrical boxes through the drywall cutouts from the inside out while not making the holes so big that the wider, outside lips of the electrical boxes can't properly provide contact to the drywall so it can be tightened via the screwed wings? I really don't want to mess with the already wired boxes. Every youtube video I find when searching this problem involves someone replacing or moving an electric box that either hasn't been wired yet or is re-wired. Any help would be appreciated.