Steph, I tend to do that, too. And, like your late darling, I do not KNOW I am doing it, nor do I do it on purpose.
I have wondered and wondered about this, and finally sort of felt that because I was born an army brat and moved around like crazy until I was 19, and heard so many accents and versions of speech wherever I was because everyone was from somewhere else, that something in my brain recorded all the sounds and used the one most pertinent to the person I was speaking with. I don't know. I truly don't know. But that is all I have been able to come up with.
My 2nd husband used to laugh while telling people that when I went home for a visit to Stephens City, Virginia in the Shenandoah Valley and came back to my own home again, my from down home accent was thick for at least a week!