If you go with migratory lids, you don't need the conventional inner cover. Instead, you can use a "hive mat" to minimise burr comb sticking down the lid, shelter the cluster from moisture and help to maintain their subdued light etc. Raid your local floor covering store for any of their unwanted floor vinyl sample books - I tried this today, but missed the shops' garbage run by a week or two
Cut yourself some pieces to cover the top bars of the top super, but leave a gap around the edges to allow airflow and give the bees access above the "mat". The gap will also let them smell the smoke puffed in under the lid. 12mm or so all around should be good, but if you do a search for "hive mat" you should be able to find some pictures to get a better idea. The mat will peel off nicely when you do an inspection and is easy to clean. I have heard of some people using some clear plastic film instead of the floor vinyl (you could effectively spy on the bees through the clear plastic!), but I haven't tried this myself.