Since trip is "last minute" I am assuming in next month or so.. so I wouldn 't worry about waiting for hours. First off waits even in summer usually only stretch to 1.5 hours or so.. BUT summer before last they had a broken elevator that made the waits 3 hours long.. that was freakish but unusual.
The other thing is you can avoid a long wait be going 1/2 hour before it opens.. or by simply getting in the MUCH shorter line for the stairs.. The stairs are actually a fun and novel way to go up the second level.. cheaper too. And years ago I went and the line for the Tower was over an hour long.. ( they had a rope marking the point saying "wait from here is one hour" ) and my son and I went to stair line and waited less then 20 minutes.
I would also consider an evening on a nice dinner cruise .. look at the Calife Cruise.. well reviewed.. I am trying it this summer after friend and poster on another site whos opinion I respect did it and gave it the thumbs up.Unlike most other dinner cruises the food is prepared onboard and not just shipped on cooked to be reheated like many of the larger dinner cruise companies.
I went to the Moulin Rouge years ago.. and frankly that was a few hours of my life I will never get back.. and its not an activity that any local I know has ever bothered to do.. and I have family and friends who are Parisiens.. its a tourist trap .. no matter what the history was.. its not that anymore. Its a cattle call. Blah food, hugely over priced, and you will sit elbow to elbow at row banquet tables.. with literally bus loads of other tourists.. and I do mean busloads.