For sure (again b’evieved to M’B, Aruch Hashulchan, many other non-Chasidish poskim) 13.5 minutes. I found that Rabbi Doniel Neustadt says 20m because we are concerned that Tzeis is 35 minutes after shkiyah and the M’B cited above says 15m before. Reb Moshe says 30 minutes (can someone find that teshuva). It seems pshat from the Rema, Kitzur, Rav Yosef (cited in article by Rabbi Flug from YU), others that Mincha is until Tzeis Hachovim. Therefore the time one states a fast ends (which is hypothetically earliest time of tzeis as opposed to motzei shabbos which might be longer as a chumra) is for sure ok according to those poskim. In other words, let’s say person waits 42 minutes then until then.
As stated in the Rav Neustadt article, the Biur Halacha says one should have a tenai that if its too late for Mincha, then the shemoneh esrei can be for maariv, and maariv will be a nedavah.
Being as 1) Mincha is d’rabbanan (so more lenient in regards to machlokes) 2) a big inyan to daven – there is a lot of room to be makel after the fact. Of course, one should daven in a timely manner (unless maybe if their minhag is otherwise) but after the fact I personally do not see why one should be machmir not to daven. I think (again assuming adverse circumstances) that one who is makel has what to rely on and if their heart is l’shem shamayim (ie they want to daven even though they “dont have to”) then go for it.
DQB