There are two parts to this question, and I've added two more questions:
1) Is there such a thing as a runtime query in JQL or in a Filter?
2) If so, can an issue date (not date/time) field be compared with the runtime query? I figure the JQL would read something like this, with startOfDay and endOf Day being replaced by the runtime Query syntax:
"PR Move Requested Date[Date]" > startOfDay() AND "PR Move Requested Date[Date]" < endOfDay()
I also figure that the JQL above would work if the filter were run on the date equal to issue."PR Move Requested Date". (The two comparisons are needed because the comparison entities are date/time.)
3) I don't suppose there's a date (note date/time) comparison entity.
4) If this can't be done with a Filter (and Dashboard that uses it), can it be done by other means, without 3rd party apps?