Hello,
My recommendation is
1. create two collections for start and stop time dropdowns (note) I am assuming that as people load this, you need to figure out which times are already used and then use the Remove function to get rid of those in the UI.
2. as people select times use Remove(duplicateCollection, TimeValue = AlreadySelectedValue) when one gets scheduled
Since the Start and Stop time Items properties are set to these duplicate collections, as soon as one gets removed it will go away from the dropdown.
The only thing I see if, what if multiple people are doing this at the same time, and one person has been sitting there a few minutes and doesn't realize that a time has been used, because the UI won't know it (for them), you'll have to make sure on the back end that you validate that the time isn't used, and send back and update set of values (or make them reload the dropdown with available times).
So your big issue is, you won't easily be able to show stuff that is "gone" unless you use like a timer to check and update the collections behind the scenes, or as mentioned, when they submit, it will fail, then update.
Also, depending on how you do this you wont need #1, you'll only need to create the two collections
