Product review (5 stars): A right-hand pump for a left-hand washer? It's secretly ambidextrous. Read on!
So, the pump arrives. The outlet is on the RIGHT side and my washer's outlet is on the LEFT side.

Oh dear.

So, off to the appliance parts store and they produce ANOTHER pump ($75) with the outlet disappointingly on the right. But their computerized exploded diagram notes "On some models you will need to configure the replacement pump to match the old pump's outlet port direction and reuse the old mounting bracket."

"How do I accomplish that?" The folks at the appliance parts store were certain that the hoses would reach far enough that no reconfiguration would be necessary. Don't believe a word of it. You'll put a kink in the waste hose if you do that.

Instead, look for a You Tube video "Washer Drain Pump Replacement  Frigidaire Washing Machine Repair (Part #137221600)" which will show you (in addition to the entire replacement procedure) how to rotate the pump's outlet port 180 degrees to match your left-handed washing machine.  The outlet re-orientation procedure begins at 3:18. Additional note:  My pump mounting bracket nuts came off with an 8mm socket, not a 5/16" like the video promised.

The plastic shroud doesn't fit nicely once you rotate the outlet port. Since the new pump has everything encased in plastic (the old pump had some very businesslike metal portion of the electric motor exposed) I'm leaving the shroud off.

The motor is quieter than the original and doesn't make that awful racket the old one was beginning to make more and more often.

Victory. Bring on the laundry.