How about this:
There are five closed primaries held on the second Saturday of Feb, Mar, Apr, May and Jun. RATS and PUBS vote on the same day. (This splitting the voting onto two different days is stupid and costs the taxpayers a ton of money.)
On Dec 1st before the Jan 1st when campaigning can begin, there is a random draw among the 50 states. Those drawing numbers 1-10 will have their primary in Feb, 11-20 in Mar, etc. This give the states having their primary in Feb two and a half months to prepare. Should be plenty of time.
I know there are more than 50 primaries as Wash, DC has one and I think PR has one and maybe Guam, etc. But you get the general idea.
I also think this would be much easier on the candidates.
Another thing to consider is having all candidates who want to run to announce on Dec 1st. Can’t announce before Dec 1st and can’t campaign before Jan 1st.
One thing that nags at me is that the large ‘liberal’ states like New York (where I currently live) and California, states that usually do not vote republican, have such a disproportionate impact upon the nomination process. I would prefer that their impact be spread out.