I think a good 66+% of “independents” are really Republican, or, like me, votes Republican nearly all the time. I am “independent” because I Cant stand being a member of the Republican Party, I dont much like them as it is, and in the world today, being found out as being a Republican is probably bad for you.
It's understandable, but ...
Unless you are registered R you can't vote in the Republican primary elections. Primary voting is the way to change the party.