Ashkenazi hoshanot schedule when first day Sukkot is Monday

Question

When the first day of sukkot is a Monday, the following is the standard Ashkenazi hoshanot schedule for the first six days (found in all siddurim/machzorim that I've seen and e.g. in Levush here):

1. Lema'an amitach
2. Even shetiyah
3. E'eroch shu'i
4. Om ani chomah
5. E-l lemoshao't
6. Om netzurah

I understand that 1. and 2. are said as early as possible, and 3. is said on the first available day of chol hamoed (consistent with every other year (see e.g. Levushei S'rad here)). I understand that on shabbat the relevant hoshana (6. om netzurah) is recited (consistent with every other year).

My question is about the relative postions of 4. and 5. Why does om ani chomah precede e-l lemosha'ot?

I understand that in such a year, adon hamoshia cannot be recited, as it is only ever recited on the sixth day of sukkot, which in this case is shabbat.

But why is its substitute om ani chomah (which is only ever customarily recited in a year of this type, notwithstanding Eliyah Rabbah here) recited before e-l lemosha’ot? Why not recite it afterwards, in the same way that every other year adon hamoshia is after e-l lemosha’ot?

[It's possible that there's some reason that would specifically link om ani chomah to the fourth day of sukkot and e-l lemosha'ot to the fifth day, but that seems somewhat unlikely when we consider a year where the first day of sukkot is a Tuesday, in which case common practice is to recite e-l lemosha'ot on the fourth day of sukkot and not recite om ani chomah at all.]

In summary, please explain why om ani chomah comes before e-l lemosha’ot.

Answer 1

It's nothing too deep. E-l lemoshaot was instituted for the fifth day of Sukkot, as it is practical to be said then almost every year. Om ani Choma is an extra, said only out of necessity in a year like this one. It is therefore said on the fourth day, which for other technical reasons doesn't have any fixed nusach.