If you are flying out of Delta on WN, you should be able to still use the priority security lane if you are Medallion gold or higher. At Denver it's a common security checkpoint for all airlines. Once I had an IRROPs situation with WN where I was forced to spend the night in DEN and the next morning I just went through the priority lane and they saw my platnium luggage tag on my rollerbag and didn't say a thing. Just make sure you have your luggage tag visable or your medallion card handy to show the checker.

Same with MDW. Just show the ID checker your medallion card and they will let you right through even if you are flying on WN.