Thanks Alan.
In doing some additional testing, and reading up on parameter sniffing (https://www.brentozar.com/archive/2013/06/the-elephant-and-the-mouse-or-parameter-sniffing-in-sql-server/), I'm finding that the following code addition makes a significant performance improvement (5 minutes to...

Here is the code for the UDF:

CREATE FUNCTION [dbo].[fn_Get_Date_Params]
(
    @strPeriod varchar(254),
    @dtmStart_Date datetime,
    @dtmEnd_Date datetime,
    @dtmGetDate datetime,
    @intWhichOne int
)

RETURNS datetime

AS