Formula - able to update to point to a tab based on a cell?

Please see attached.

Okay, so I'm tired of updating my formulas whenever a new month roles in. I was wondering if there was an easier way. On the attached spreadsheet there are three tabs:
Data - this calculates the tenure (and what I want to most update).
5-31-19 - this is the material that the 'Data' tab is currently calculating.
6-30-19 - this is the data that I want the formula to calculate BASED on what is in 'Data'!K3

So one of the formulas is this:
=COUNTIFS('5-31-19'!$E:$E,Data!B$1,'5-31-19'!$D:$D,"<1")

Instead of having to alter the formula to capture the new tab (ex. =COUNTIFS('6-30-19'!$E:$E,Data!B$1,'6-30-19'!$D:$D,"<1") )
I would like to be able to do this:
=COUNTIFS('Data'!K3$E:$E,Data!B$1,'Data'!K3$D:$D,"<1")

Or something similar?

Is that possible?

I gave you a reputation point and indicated that what you wrote didn't work - but it does. My mistake.

I had to change K3 to TEXT and then input 6-30-19

Works like a charm!