I have this too. It's like not being able to visualise what my mind is talking about forces a stutter. If I am upset I will get stuck on one sentence for hours or days just repeating itself. If I don't know where my sentences are going I will elongate words (exxxxaaaammmppleee) like sounding out, repeating/stuttering words etc.

I, too have visual aphantasia, but constant dialogue. It can be frustrating if I am in a bad head space because as I said, I can get stuck on one singular thought and can't break the cycle.

Yours sounds worse than mine, in the sense that my inner dialogue is insane, never rests, never stops (I have to sing songs to stop myself from thinking anything otherwise it never ends) but if I am unsure of why I am talking, what it's about, in a bad place, anxiety etc I have the same issues you have stated. Most probably not as severe, but definitely noticeable affecting my day to day when it happens. (I have always been a huge reader, very wordy and poetic so that may be why I don't have as much of a struggle on the day-to-day as you do).

Sorry I can't provide any tips on handling it, but at least we aren't alone.