Hi BumbleB, and thanks for the reply!
I have contacted Samlesbury several times about the paintings, and only once did I ever receive a reply. They stated that they didn't know who the paintings were supposed to be of and did not have any records of them ever having been purchased....
I find it somewhat hard to believe that absolutely nothing is known about these paintings, and I still hold out hope that someone can figure this mystery out. Being in the States, it's a bit hard for me to do some firsthand sleuthing of Salmesbury and the Lancashire area, so naturally, I was super excited to find this forum!
The reason it's of such interest to me is that Edward and Alice Southworth are my 10th great grandparents, and Samlesbury Hall is the ancestral family home of the Southworths. I came across the supposed painting of Alice very early on in my genealogical research and was excited at the possibility of a painting existing of someone so far back in my family tree. However, I quickly learned that it was not for sure a painting of Alice and wanted to to do some research myself to see if it was or wasn't.
Unfortunately, I've only hit dead ends. At the very least, if a signature on the portraits is visible, that would be something to go on. Knowing who the artist is could help narrow down who the couple is.