ST, you might want to get a couple of good ratchet straps to hold everything together. When I'm hiving a swarm I like the bottom board stapled to the bottom box, but I might stack another box on top of that one along with the cover...the ratchet strap makes me feel more confident that everything will stay to gather while traveling.
I have plenty of ratchet straps. 1 to wrap around each, 1 to hold them down and 1 to keep them from sliding.
Also, a piece of #8 mesh screen 3-4 inches wide by ever how wide your entrance is is good to block the entrance. Fold it in half the long way and push the folded edge into the entrance. The tension and friction fit should hold it it place but you can put a staple in it a couple of places for insurance. Also, an inner cover with #8 screen over the hold would give them more ventilation. It is surprising how much heat they can put off.
I have SBB that I was going to close up. I figure there will be enough cracks to keep them ventilated. I was going to tack on the entrance reducer and plug it with grass and a piece of tape. I'm glad you reminded me, I didn't think about the inner cover, I'll tack a piece of screen on that as well.
The hives are going to be in the back of a pick up, at night, with temps around 40-50, traveling at 65 mph. I'm hoping that any air that gets in, isn't going to be too much for them.
If you have to end up cutting the comb and installing it into medium frames it really isn't a big deal. The cut out pieces would fit nicely being as the shape is already squared off and one dimension is the correct size...it would not be nearly as difficult as doing a cut out from a wall or something. I would use two medium boxes to do the cutout...cut a piece from one of the deep frames big enough to fill a medium frame and install that frame in the lower box then put the remaining piece of comb from that deep frame in another medium frame but install that frame in the top box positioned directly above it's original lower part. That way the comb still has the same configuration but in two frames. You most likely will have 2-3 frames per nuc of brood comb to deal with if you decide to do a cut out....not all five frames....but, maybe you will.
I really don't want to cut the comb and lose any brood, but that may turn out to be the best thing to do. It'll set them back on building new comb while the repair but it'll be 10 frames in the mediums that'll be filled faster.