There is no way to add a scroll to a select field other than to have lots of entries (as our demo does). What you could do is to make it a combobox in the field settings. This would the apply the Select2 jQuery script to it, and style it much better.
At the moment you are hiding if empty. But you want to show them, see here:
https://www.screencast.com/t/jUc9Mhe5WqYf
Some custom CSS is needed for the date to be in 2 columns:
.searchandfilter[data-sf-form-id="14110"] li.sf-field-post_date input {
width: 100px;
min-width: auto;
display: inline-block;
}
.searchandfilter[data-sf-form-id="14110"] li.sf-field-post_date li {
display: inline-block;
}
.searchandfilter[data-sf-form-id="14110"] li.sf-field-post_date li:first-child {
margin-right: 20px;
}