There is absolutely zero chance you will achieve truly flat with a belt sander.
Completely aside from big-picture questions like "What is flat - if it isn't a straight line average between the current height of the edges?" , any pressure you put on the belt will cause both elastic rebound inaccuracy (both from the base and from the belt/pulley system) and thermal (overheat) inaccuracy.
The competitive side of me wants to take that bet, but i'm a ringer. & one of my larger machines has water coolant.
I can see making it work fairly well by adding end guide/supports, possibly a large radius (end to end) platen, using flood coolant, putting a VFD on it, and slowing the speed to a crawl while stroking the ski "with practiced skill" manually. Essentially an older version manual stone grinder.
Without practiced skill, you might loose a few skis dialing the speeds and motions in.
As has been pointed out, thermal issues are a very difficult factor. Metal and plastic expand differently.
The very first widebelt sander ("Planer" style/feed-through woodworking or metal conditioning machine) i ever saw arrived in a friend's shop in the mid 70's from some ski manufacturer. I suspect Head, as they had been local in Baltimore a few years before. Unlike actual woodworking widebelt machines, the belt was underneath the work, and the single top roll/feed roll was weighted, & rose & fell to accommodate variable thickness.
OTOH, back in those days, it seems many manufacturers' skis arrived railed due to somewhat similar base flattening ops. Where the conflict between multiple sources of differential expansion and differential response to any given abrasive is rife.
I have a shop full of abrasive machines, and prefer to just file and stone my skis as being faster, floor-to-floor.
When you get into race tuning, it is even more complex.
Could it be worth teaching the kids to maintain & tune their own skis with manual methods, like they had to learn in the old days?
smt