As an alternative to a Prime time button Radio times
has a very convenient pair of Jump bars that allow single click navigation to any time of day or day in the
Something similar could replace date picker and the other earlier later buttons.
Borrowing liberally from the example MymsMan provided, here's one I knocked up last night. It's there now if you want to experiment with it - as the red text says, you can change the number of hours across the screen by holding down the 'Control' key and clicking on a new end hour. It will limit you to 8 hours in total though.