I understand the appeal of the original movie. The adults saw the satire, same as Holy Grail and Life of Brian. The kids caught the zaniness, the antics of the bandits. But what really caught my attention as a child sitting in the theater during the premiere was the map itself. What else did that map show? Where could you go? Anywhere.
That is what the series should cover. They don't have to include anyone from the original movie, they just have to have the map. Maybe Kevin will find his polaroid image of it as an adult and go on some adventures? Maybe his kids will find it after he "disappears", Flynn-style, and go off in search of him?
For the folks who are aghast at the idea of a cherished, perfect movie that encapsulates a particular time in their life getting remade, I get you. Really, I do. The Star Wars prilogy walked across our psyches (and I wasn't even a fanboy of the originals). Blues Brothers 2000 - lets not even go there, and right now we get the paper-thin facsimile of MacGyver. What are the chances that a Time Bandits series isn't going to suck? Not much, I'm afraid. It could turn out a steaming pile of crap, like the Librarians. But as was mentioned earlier - Stranger Things? Did someone manage to absolutely nail early-80s midwest America? Yes they did.
So, take heart in the fact that Apple has a huge war chest full of capital and wants IP that will produce dividends, ignore the fact that its run by a bean counter with a social agenda, and hope that maybe the idea I posted up above is the way it goes. Or maybe come up with your own idea to hope for and post it here so we can have something positive to talk about.