Do you think that if I call Southwest Airlines Customer Service and
asked them for the tail number of the aircraft that flew this leg they
would volunteer the information?
No. Tried it. If you call customer service, they won’t give it because they probably don’t have it. If you write Southwest, they won’t provide.
You can wait a couple of months then go to the Bureau of Transportation Statistics to look it up.
Edit: changed the link to show the direct link to airline information.
You could also try looking at an ACARS database to look the data up. More immediate than waiting for the government site to update, but data can be incomplete.
Is it the assent potion of the flight everyone is interested in?