Your example sentences use we/us as personal determinatives, in their terminology, so that principle applies, with "We girls gotta stick together" being the norm and "Us girls gotta stick together" being found in colloquial speech or certain nonstandard dialects.
If "gotta" is equivalent to "got to," and "gonna" is equivalent to "going to," adjusting the spelling is allowed, but further alteration for grammar ("have got to" instead of "got to") isn't. Meanwhile, if gotta is important to capture the "tone or sense of place," use it unchanged.
When quoting someone, is it proper to change "gotta" to "got to ...
While watching American TV series, I sometimes see a sentence, "I’ve gotta go," but sometimes an actor says “I gotta go” instead. Is there any difference between those things?
differences - “I gotta go” or “I've gotta go” - English Language ...
You Gotta Have GUTS! Stuff You Gotta Know: Straight Talk on Real Life A Guy's Gotta Eat A Woman's Gotta Do What a Woman's Gotta Do The Teen Girl's Gotta-Have-It Guide to Money Uh Oh! Gotta Go!: Potty Tales From Toddlers and, my personal favorite: You Gotta-Wanna (a book about sales advice)
formality - How often do people say "gotta", "wanna" or "gonna" in ...
I often heard people say the word "gotta". I have read in this web site that gotta is a contraction of "I have got to" and that that phrase means "must", is my understanding correct? Regarding the...
expressions - meaning and use of "gotta" - English Language & Usage ...