Thing is, if the magic-wielders are few, then they'll have their own soldiers who do all this mundane stuff, too, only augmented by magic. If they are not so few, they'll still have soldiers, but there will be plenty of mage-soldiers, and they'll still augment magic with whatever mundane techniques are around. So, you need really big numbers, massive imbalances in commander competence, or the Steel Rebels need to hit the magical dudes when they're already down. Your demographics don't fit the overwhelming numbers idea (and given the advantages of magic, it'd need to be order-of-magnitude superiority). So you're down to making the rulers of the world incompetent, or you're finding a way to weaken them so they're vulnerable to what should be an easily dismissed threat.
Don't want anti-magical materials? Well, what about a once-in-a-few-thousand-years astronomical conjunction that suppressed the power of magic for a few months? No way from anyone in the modern world to get their hands on that. You could even make a loss of magic a result of a terrible spell failure result on a massive ritual, if you want the Sorcerer Princes to have paved the road to their own downfall.
Maybe the Steel Rebels focused on the healers to start with and managed to take out enough that there were no longer enough to nip budding plagues in the bud and the cities were ravaged by disease, collapsing civilization out from under the magical rulers?
Maybe the mages were already worn down from another war. Could have been a civil war. Could have been an invasion from another dimension, another world, or maybe rampaging dragons (though this would leave the surviving magic-wielders quite experienced, as well as their own soldiers).
How do the luddites have better tech and more cash than the folks with their hands on the means of supernatural production? That sounds like the previous suggestion going on now, but by proxy. And so what happened to these powerful backers who surely would have moved to step in and take over after the existing power structure was out of the way?