If you question whether a relay is working the quick and easy way would be to swap with another one. You may find that your relays are fine and the problem is a failed component and NOT the relay itself.
How many miles do these cars have? There are obviously different opinions as to using the Dex VI in an old transmission but I like to err on the side of caution. Do you know when or if the fluid had ever been changed?
Judging from what the OP said in post #7 the mechanic is an honest man. He could probably do the job but he is looking out for his customer's best interests. At 300k miles the rest of the vehicle may be on it's last legs and not worth the time and expense of either a costly head job or even...
On the tranny just do a pan drop with filter. NO FLUSH. At 165k miles I would just clean it up and drive it. If you want a supercharger buy an Ultra. The tranny on your base model would need more mods than it's worth.
As much as I like my 2002 Lesabre Limited I truly miss my 1997 Oldsmobile 88. The styling got better on the Buicks after 2000 but unfortunately the quality did NOT. The pre-2000 cars were built better IMHO.
With a car this old you are very limited with a part like that. I know you said you didn't want to go with a salvaged part but a web site like Car-part.com may be one of the few options that you have with a 27 year old car.