These are my observations.
What I posted here is the GR"A's version of the correlation between the Sefirot and the Luminaries.
- Levanah - Chesed
- Ma'adim - Gevurah
- Chamah - Tiferet
- Netzach - Nogah
- Hod - Kokhav
- Yesod - Shabbtai
- Malchut - Tsedek
This is at odds with the order of the 7-hour cycle:
That is to say, Tsedek, Levanah, and Shabbtai have their order switched, but the remaining four, Ma'adim, Chamah, Nogah, and Kokhav, are identical.
If both lists represent the ordering of the Sefirot as this:
Then we are talking about a change like this:
- Tsedek - Chesed / Malchut
- Levanah - Yesod / Chesed
- Shabbtai - Malchut / Yesod
Tsedek and Levanah would seem, therefore, to be related to Chesed through different points, Tsedek through Malchut, and Levanah through Yesod.
The GR"A explains there that the 7-hour cycle, which actually starts with the last one I've listed, Shabbtai, and then Tsedek, etc, is the order from top to bottom. Shabbtai is the beginning, since it is the first one to "serve" when the luminaries were created at the beginning of the 4th night.