Al-Nahar should mean daylight because the context in verse 37 talks about darkness when al-nahar is removed. It is the analogy of removing guidance from the disbelievers so they are made spiritually blind … one needs light to see … not the sun.
Manazil - plural of manzil = ranks, stages or phases - as you say most likely phases of the lunar cycle.
Tudrik = overtake
Saabiq = outstrip
The fact there is always a set number of days in each lunar cycle means that this is a sign … there is always 29 or 30 days and this will never change. The days in a solar year do change that is why adjustments are required every 4 years then every 400 years. However, not so with the lunar phases.
We can conclude at least that the night/day combo is Saabiq and the Sun/Moon combo is Tudrik which means the words should not really be translated as equivalent.
Totally agree with the contention with the term “orbit”
Wa Qullun Fi FALAK inyasbahoon
And All are in a floating cycle
Falak = cycle “orbit”
yasbahoon = floating
Compare with Surah An-Naziat:
Was Sabihati sabha, Fassabiqaati sabqan …
And those who swim swiftly along and those who press forward
Interesting how outstrip is also used for accelerating or pressing forward and how sabha seems to take the meaning - suspended/floating/swimming.
Compare with the next verses in Surah Yasin and we have a boat on the water … is that like the Earth in solar gravitation field?
The questions are amazing … so imagine how amazing the answers will be !!!