Some equipment I have worked with used inner covers and telescoping lids, presenting the problems you describe.  One solution is to use a inner 'blanket' made of oilcloth (plastic side down), black plastic, or other such material.  Defeats some of the purpose of using inner covers, but makes removal of innercover/telescoping lids easier/possible.
 
My own solution is to use migratory tops.  Plain plywood (5/8" preferred) when time and cost dictate, cleated wood (1x4's) with a beeway (I really like that beeway!) if time and money permit.  I can always get a hive tool under these, the bees glue them down nicely, and the plywood is quick and cheep so damage/loss to them is of no great concern.
Dennis Morefield
Sideline Beekeeper,  100 colonies(at times!), Oregon, USA
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