I do like the idea of requiring all primaries to be on April 15, it would be difficult to argue for raising taxes on that date.
Seriously, the federal government doesn't have to anything about it. I would prefer the parties to take action instead. The parties already do some things that could be applicable to primary reform.
Unlike the US House of Representatives, the state delegations to the party conventions are not strictly allocated proportionally to population. States that historically vote for a particular party's nominees, are rewarded with larger delegations than states that routinely vote against the party's nominees for President, Congress, Senate, etc. In the Republican Party, Texas gets a larger delegation proportionally to population than California, New York, or Massachussetts. One or both of the political parties could reward states with later primaries with larger delegations. This would mean a state would find its own self interest may lie in having its primary or convention later rather than sooner.