Why not run the primaries for seven consecutive weeks. Each week a bundle of states representing roughly 560 delegates goes to the polls. The bundles can be worked out but should, as much as possible, represent some geographic diversity, in fact the maximum that can be achieved. Each election cycle the order rotates as to which bundle goes first, which second, and so on so that after seven election cycles each bundle has been in each weekly slot.
I know, the states set their own schedules. Things, however, do change.
I agree that the schedule has to change. But any new system is going to have winners and losers. The seven-week sprint you propose would likely benefit candidates with lots of money and name recognition and prevent someone from rising organically.
Here's a question: if you assume you want to start the process out with some level of retail politics, is there a smallish state with a diverse population, ideally a swing state so that all the organizing work parties do beforehand doesn't get tossed in the trash as soon as the primary is over?
Looking at a US map, nothing perfectly fits all those criteria, but I think Minnesota/Wisconsin come closest. They're not small, but they're also not dominated by major media markets that would suck up all the money (although I suppose SE Wisconsin overlaps with the Chicago media market). Oregon could also potentially work, but it's not very swingy.
Other problem with the rotation idea is that it assumes all elections are basically the same. If there's an incumbent president running, the states that go first have basically "wasted" half of their opportunity. You also may see politicians gaming the system, particularly if the rotation is based on regional groupings (which you're not proposing here, but which I've seen others touting). So Kamala Harris and Elizabeth Warren are both eyeing the race, but Harris knows that this is a "West Coast" year, so she can get in the race and get an early boost from some easy wins in CA, OR and WA, while Warren doesn't get to her home-field advantage until the last group of primaries, by which point she's likely to be out of the race.
Anyway, not trying to crap all over your idea. I just suspect fixing this is going to be a lot harder than it looks.