Why not cover the glass cooktop with a couple of large wooden cutting boards, to make some counter space that you don't need to worry about, then use a two-burner countertop cooker with your new pans?
Don't know why your new pans would be unusable for a glasstop cooker, unless they are uneven or scratchy in some way. But I'd believe the warning, especially since the stovetop belongs to the landlord.
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