You don’t need to eliminate primaries, you just need for all primary states to restrict voting to registered in state Republicans. (I put in state as a requirement because incredible as it sounds New Hampshire allows out of staters to vote in primaries)
States like GA have no party registration. You simply walk up to the voting desk and ask for a Democratic or Republican ballot.
I doubt you could get a state like GA to start registering people by party, much less requiring you to be a member of one before voting.