Options to move the school rucksack during the trip
I've always commuted to school (and subsequently to work) by bike, and my method was: none of the methods mentioned in the question.  I'm from The Netherlands, and grew well into adulthood (and lived in other countries) before I realised that arriving to school like this is not the norm in most of the world.

I had permanently attached to my rack a set of heavy-duty luggage straps, then I would attach my backpack to this.  I think the straps were actually attached at the axle, so it would have required some tools to remove it.  My backpack was usually secure from falling, although it occasionally did fall or topple to the side, then I would stop to reattach it.  From memory, I think that happened less than once a month in a 20 km/day round trip commute.  I did not own any panniers at the time.  I have fallen off my bike once during around nine years of commuting to school by bike, while turning on an untreated icy surface, the luggage did not add to injury.

Later I got some Dutch-style panniers that I also left permanently on my bike.  I would put my school backpack inside one side of the panniers, and take out some books to put loose on the other side to balance the weight.

Most of my classmates simply cycled with their rather heavy backpacks.  At the time there was a fashion to have the backpack extremely low, with extremely long shoulder straps.  Some kids would have backpacks hanging as low as their knees.  I remember seeing kids with their backpacks so low, that the backpack would actually rest on the rear luggage rack as they were cycling.

I think a pannier/backpack-combination is both a poor pannier and a poor backpack, and when it's heavy it makes for an imbalance bike too, unless you can somehow convert a single backpack into /two/ panniers?