What is the best etiquette solution to handle customers at closing time at a museum?

[Hopeful future]

Every year it's the same problem. Visitors to our museum show up 10 to 15 minutes before we close and get very upset because we will not stay open for their visit. We try to give the best of customer satisfaction, but face it, a museum is not a grocery store, you are not just going to run in, grab a gallon of milk then leave. We have much to see and you can spend a few hours to experience it all.

We increased hours and still before closing you will have someone who has not planned ahead for how long it will take to get through the exhibits complain about us closing because they arrived too late. We have closed one exhibit (that takes 10 min just to reach) one hour before closing so visitors there won't feel rushed.

How do other museums/attractions handle this issue? In the past we have paid workers overtime to accomodate very rude irate visitors but it's getting crazy and very costly to keep this up. We have to close sometime. Any solutions out there we haven't thought of?