Salaam miah. I am convinced that the salaat in 4:102 can not be any education let alone quranic education because it is performed on the active war front, which is where the believers who perform it are warned by God to be on the alert and take precaution:
When thou (O Messenger) art with them, and standest to lead them in prayer, Let one party of them stand up (in prayer) with thee, Taking their arms with them:... - وَإِذَا كُنتَ فِيهِمْ فَأَقَمْتَ لَهُمُ الصَّلاَةَ فَلْتَقُمْ طَآئِفَةٌ مِّنْهُم مَّعَكَ وَلْيَأْخُذُواْ أَسْلِحَتَهُمْ .
Being on the active front during a war is like being on a raft afloat the rising waves during a flood. It is in no way a place where you can take education. It is a place where you give your dear life if you do not concentrate and if you get involved in things like education to weaken your concentration.
While your assertion that it does not mean Quranic education may be correct, your reasons against this weaken your argument for ritual prayer.
Consider an army of ten thousand. If the rasool were to per form the ritual prayer with them in two sessions, this would be the ideal time for the enemy to attack even with half on guard. If he were to lead them in more than two sessions, the time required to perform these rituals could become astronomical. This is without even taking into account the time needed to remove & put on their armour. The ritual in this instance would be extremely impractical.
It would make more sense that the salat here be in the form of briefings regarding strategy with special care being taken that the Quranic etiquette regarding war, prisoners, etc. are being observed.
Although my study on salat is incomplete, I would ask that you look at the verses where salat appears, then go back in the text to the start of the theme and forward to the end of the theme. When I did this a common thread developed which indicates that the salat is an event that is used for the purpose of ensuring that the pure message is used as a measuring stick for our daily life decisions both on an individual as well as a community level. The common thread is that in many cases a departure from or hiding of the truth is mentioned. Salat is used to keep this kind of thing in check. This is especially true when autonomous communities are formed that accept the message. Before such a community has authority, they are a revolutionary movement. Once they have authority, they tend to become just another government. This is why there are verses that exhort the reader to establish the salat if given authority in the land.
Anyway, my study is not complete & I will post in more detail once I'm ready.