Lookup name with multiple criteria & between 2 date ranges

BACKGROUND: I am working on trying to calculate surgeon's credited minutes. Doctor's are able to essentially give up their credits to another doctor for the same surgery area for the same day that they give up. E.g. If Tina gives time up on 7/4 to Mark. Then mark gets her credit for 7/4.

ISSUE: I need a formula that can lookup the name of the surgeon (RELEASE TO DR... 1) using the following info

1) date [between "start date" & "end date"]
2) surgeon who gave up the time [SURGEON]
3) service location [SERVICE LOCATION]

In the example in the workbook. IF on 7/4/2019 Tina gave up time in the AMBULATORY, the result would pull up "MARK."

I attempted and index and match function, but it ran very slowly since the formula is 365-366(total number of days in a year)*(number of surgeons long). I am trying to avoid using array solution because of that.

Any help or insight would be greatly appreciated.

Please try,

Formula:

N3=INDEX($E$3:$E$18,MATCH(1,(K3>=$A$3:$A$18)*(K3<=$B$3:$B$18)*($C$3:$C$18=L3)*($D$3:$D$18=M3),))

Note that in K3 to K5, I changed the year from 2020 to 2019, in order to be in the range in the raw data table.