Newspaper-uniting a queenless all-medium colony onto a deep colony — how do you combine mismatched box sizes?

Oregon, fifth year. My all-medium colony — the one I set up two years ago when my back started complaining — has lost its queen. No eggs for three weeks, no cells, a few laying-worker eggs starting to appear on the cell walls. Too late to requeen here, so it's getting united with my neighbouring hive, which is a strong double deep with a good 2026 queen. The thing I've never done is unite across box sizes. Both are 10-frame Langstroth so the footprint matches, but every guide I've read assumes you're stacking like on like and then consolidating the frames into one box afterwards. With medium frames I can't drop them into the deep. So: does the medium box just go on top of the deeps with newspaper between and stay there as a third box for winter? Do I shake out the laying workers first? And what happens to the medium frames in spring — is that colony now permanently three boxes?