I need to power a dryer and a sauna from the same 220v/30a breaker, but not simultaneously
Are you on NEC 2014?  NEC 400.7(A)(11) specifically allows an isolated inter-floor run between an outlet and an inlet.
However this must be done using normal and proper in-wall wiring methods such as NM-B cable, or THHN in conduit.  Your plan, to York-a-dirk it* with an SOOW extension cord, violates 400.8, and the inspector was quite right to nix it.
All this is beside the point. There is no limit to the allowed number of 30A receptacles on a 30A circuit. Route the new circuit to the breaker panel not the dryer recep.  Share the breaker.

* thanks for that, autocorrect!