It is possible you would get No. 2 --- a number of states already conduct their primaries that sort of manner (unenrolled voters can choose in which primary they wish to vote -- but you can only vote in one primary)
Numbers one and three are just not going to happen in our lifetimes.
•3. Can't ever be achieved. People get together; it's how our species works.
•2. Better the redundant and useless legislated primaries should be abolished. Let parties pick their candidates as they choose. Just make laws about honest process. Wouldn't hurt to make those apply to any and all formal groups.
•1. The Senate has the only national legislators with serious experience and a clear mandate: to represent their States in Washington. Return to first Constitutional principles and have States pick 'em as they choose. Keep the feds out of it. The House can establish its primacy by its merit. Or not.
Before you do anything: Get one decent, fair, non-partisan set of election rules nationwide, from districting to voters lists, administered with as little party influence as possible. The piggybacking pretence that widely varying state laws are all that's needed to elect the planet's most important government is way past its best before date.
And somewhere in those rules, one might think to require Electors to be free of compulsion to vote in any way, except to reflect the popular vote in their state, if the College cannot be abolished. And at least make them wear cute dress-up outfits like the Brits now and then do in the Lords, when they do their ceremonial task.