Conservatives should study how The (New) Conservative party of Canada did it in Canada.
Basically, They started another party, the Reform party, later renamed the New Conservative party of Canada, then merged with the remaining conservatives from the old party, forcing the blue liberals, the equivalent to our Northeastern Rockefellers, out.
Yep, ultimately politics is marketing and sometimes you have to change the brand name and logo.
Might be the way to do it but the country is so divided between the two parties that a competitive party might not be able to accomplish it, anymore than third parties have been able to accomplish anything except be spoilers for their philosophical allies. The Dems did it with PACs and 527s and I think that would probably accomplish a lot if conservatives vowed to starve the party and let the PACs and 527s hand out the money and/or support.