just wants to minimize the probability that she’ll be dumped,
I suspect that this is not the real objective function, as it can be trivally minimised by never going out with anyone.
Personally, if I was with someone who would dump me then I would prefer that it happened sooner rather than later to minimise my investement, especially emotional investment, in that relationship. I think the aim of the exercise is to find someone to whom you are compatible. Avoiding being dumped in this viewpoint could be counter productive as it could lead to being “stuck” in a less desirable relationship. Manipulating the other person into not dumping me does not seem like the sort of relationship that I want to be a part of.
Now I know that there is a stigma attached to being the one who is dumped. However, I have noticed amongst my aquaintances that have been in relationships that ended after a long time that the one who is dumped seems to recover quicker and get on with their life (next relationship—maybe marriage) while the dumper is still caught up with whether they made the right decision (a choice that the dumpee never had). Of course this is anecdotal and based on a very small sample.
For me the benefit of talking out loud would be more a matter of focus. I have an inner conversation anyway and so it would be just saying the same words as I am already saying on the inside (which might slow me down, but not an issue when the problem is difficult). The real point is that if I say the words then I am only going to say the words related to the problem. The words related to the distraction will not be said out loud. Therefore, making an effort to speak out loud means that there will be more focus on the problem because allowing my focus to wander onto distractions more obviously results in silence.
I definitely notice that it is at times when I am most struggling against a distraction that I start talking through my problems out loud.