If I was sick all day and was unable to put on Teffilin during the day, may I put it on at night to make up for the day I missed? If I remember correctly, the Mishna Berurah says that if one will not be able to put them on during the day he may put them on before Alos hashachar. Is there any basis to allow putting them on at night? What if I slept all day thus mitigating the concern of Falling asleep with them on and coming to flatulence, would it permitted then?
Rav Ovadia Yosef permits putting them on Bein Hashmashos with a Bracha (source), which is interesting given that the Rambam implies it is an issur dioraisa to put them on at night (Tefillin 4:11), but Shulchan Aruch (O.C. 30:2) does not pasken that way, and leaves it as equally rabbinic to leave them on or to put them on (or actually more of a problem to put them on).
If, however, one has already davened Maariv, even if it is still before Shekia, Shulchan Aruch (O.C. 30:5) says to not put on Tefilin, and Rav Ovadia Yosef paskens to put them on without a Bracha (during Bein Hashmashos), apparently agreeing with the Magein Avraham there as well as the Shulchan Aruch HaRav (O.C. 30:5).
The distinction between the above and the case you quote in your question, which is the Din in Shulchan Aruch O.C. 30:3, is that when it is before Alos HaShachar it is being done for the morning, but even then the Magain Avraham limits this to walking, not sitting in a coach where one may fall asleep. Rabbi J.B. Soliveitchik is quoted here (link downloads a file) as saying the distinction is that when the Tiffilin is being put on for the sake of the morning, even before Alos HaShachar, it is OK because it is for the sake of the day time, which would not be the case if you are putting it on at the beginning or middle of the night.
So from all of this you see that actually putting them on at actual night time is not permitted. There is a dissenting opinion in Rishonim (I have seen Rabbeinu Yona quoted as one) - that the idea of הלכה אין מורין כן (discussed in the above sources) applies even to putting on Tefilin at night, so the whole rabbinic prohibition - according to that opinion - isn't that strict, it is more about how people in general should be trained rather than a strict prohibition.
Here Rav Ovadia Yosef is quoted as saying that a soldier in a non-Jewish army that is simply not allowed the opportunity to put on Tefilin during the day light hours should put them on at night without a Bracha.