So, if this is the case, I figure that the following should work:

Add a new printer and set it to the same properties as my default HP Laser printer.
Name the printer "xxHP Laser" or "zzHJP Laser" (make sure it is on the bottom of the printer list).
If what you are stating is true, then this should be the printer automatically selected when I print from an ePrint PDF document, and all I have to do is click OK or press <ENTER>.

What do you know? It works!
And my default printer is still the regular HP.
So, your investigation helped to discover a work-around!
Thank you!