You're looking for a dynamic parameter, which we still don't have. (There is a large discussion in the IDEAS forum. Your use case is one of the most common needs for this.)
They're working on it.
On some dashboards I've added an extra parameter layer. I give the user choices of
"Last Closed Date" (same principle as your requirement for "Today")
"Range of Dates"
My published default is "Last Closed Date", so that's what they get right up front.
If they choose "Selected Date" I pop out an additional parameter that lets them select a specific date.
If they choose "Range of Dates" I pop out two parameters to give a start date and an end date.
Then I use calcs that look at the first param, and then decide what dates to give the user based on that selection. If they choose "Last closed" I grab whatever date that is. If they choose "Selected Date", I grab that instead. Etc.
It's extra work for me, but a pretty user-friendly UI for the user.