You can create custom dropdown to have just the dates (you can fix some range like like up to last 1 year) for the range and custom fixed Hour dropdown. The complexity will come on how these dropdown values will be used, and that depends upon your queries. Can you post what type of queries you're going to use?
I'm a tech writer here at Splunk and I'd like to help. Have you tried using a dropdown input for this panel? Here are some documentation resources for inputs and time specification:
This previous Answers post also seems to cover something similar to what you're trying to do:
I hope these help! Please let me know if not and we can continue discussing.
All the best,