"Because we're trying to remove the Democratic Party from existence."
You don't do that by telling voters that they are not allowed to vote for the candidates they like. The GOP was able to rise in Alabama because it allowed candidates to be as conservative as they wished, while the Democrats were forced to kowtow to liberal interest groups for fundraising and DNC support. If the party bigwigs start telling people that they are not allowed to vote for X or Y candidate, all those gains will be for naught.
Just let the GOP primary voters nominate their favorite candidate. You already have the advantage of having a run-off when no one gets 50%+1 in the primary, so you won't have to worry about a fringe candidate in a multi-candidate field winning the nomination with 30%. The voters will select the candidate with whom they most agree on the issues, which is really all you can hope for.
BTW, GOP dominance in AL has not yet reached the state legislative level, so instead of kicking candidates off the ballot maybe the GOP should work at electing Republicans in conservative districts so that the party can control the legislature and be able to draw fair districts after the 2010 Census.