Can a man pray in congregation with an alien woman in a house in the presence of a unmarriageable woman who is not praying due to her menses?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Your prayer as you mentioned in your question is correct. Presence of an unmarriageable woman with you prevents you from being alone with an alien woman. But we believe that since this woman is marriageable for you, it is better that you not pray in congregation with her, especially since she is the only woman praying. In such a case, it is preferable for each person to pray his/her own prayer individually.
Permission in such a situation is only if there is no temptation for either of you. If either you or she feels tempted by praying there, then it is forbidden, particularly if both of you are young.
Dear brother, we advise you to pray in the mosque, if it is possible. Since the Prophet has emphasized praying in congregation. In a Hadith a blind man asked permission to pray at home. The Prophet said to him: "Do you hear the call", when the blind man said: "Yes", the Prophet replied: "Answer it; I do not find any authorization for you". [Reported by Muslim].
The Prophet also said: "Prayer in congregation is superior to a prayer performed individually by twenty seven degrees". (Related by Bukhari and Muslim).

Allah knows best.