Naah, there's a perfectly American and indeed Republican way to deal with this. You need a grassroots movement like the Tea Party which primaries RINOs and helps candidates who pass the purity test into power.
It's true that the Tea Party was eventually co-opted by the Republican establishment but not before it had managed to pull that establishment significantly to the populist right.
Also, I think the current Republican establishment's chance of co-opting a grassroots movement is significantly less than it was back in the Tea Party days. Back then the argument was about ideological purity. Now it's about whether or not you should betray the party and put the Democrats in power after they ballot stuff. All the Republican establishment figures like Kemp and Raffensberger are screwed in the long term unless they can convince the Democrats to let them defect. And the Democrats don't want them, they want Stacey Abrams.
And then there's Lin Wood and Trump
threatening to put them in prison for electoral fraud and/or plotting a coup with foreign backing.
If I were an American right-wing populist I'd organize primarying all the RINOs in the Republican party and replacing them with populists.
Incidentally one of the interesting things about some sort of RNC/DNC deal is that neither can admit to it. So if you're a Kemp or a Raffensberger and some populist runs against you on the grounds that you betrayed the party you can't just say 'Betraying the party is such an exoteric view. Insiders know the esoteric truth that there's a behind-the-scenes deal here. You rubes just don't understand that. I bet you think Pro Wrestling is real too' because they'd sound insane to most people and the people who believed them would still consider them traitors. This is the reason they've done everything they could to avoid having the GOP legislators, most of who take the exoteric view, from voting on it.
When your opponents have a position that is literally indefensible it seems likely you can unseat them in a primary.