ATWT was not Moore's first acting job. She had been on EON previously.
Also, when Moore first arrived in 1985, her first year, I actually thought the character had a dour, melancholy undertone. Grown-up Frannie was clearly hiding the effects of a breakup from a tumultous relationship when she arrived in Oakdale.
If you remember, she and Barbara had a mild falling out because Frannie didn't show up for her fittings for Kim's bridal party and was cut out of taking a vital role in Bob and Kim's wedding.
In terms of why Sabrina might have stayed around so long (she outlasted JM's run, by the way), Marland likely saw Moore's work on EON and somehow thought she had a facility for accents, since the character she had played on EON had one. I don't understand the reasoning but he may have thought that it was a nifty skill to have somehow.
In a way, he wasn't that far off-base, by the time she did A Single Man with Colin Firth her British accent had improved to a level of authenticity.
I once saw her on a TV show look at a clip of herself as Frannie and Sabrina and she cringed at it and I do think it much to do with the accent. She also joked about the fact that her aunt had married her father and her twin was actually her cousin and laughed and said "The Hughes were the nicest people but...I know...that's so disgusting, right?".
I do think that by the time MES had gotten into the role, the writing for Frannie was a little more nuanced and the stories less bizarre, probably because Frannie was an older, more mature character than she had been when Moore portrayed her. The other aspect is that we mainly only heard about Sabrina and didn't really have to physically see her onscreen during MES' tenure. A huge difference in the load that the actress has to carry.