Simpler solution — Congress can just make voting mandatory, as Australia has done. It works. They could also require states to use ranked-choice voting. Both moves are legal and do not present constitutional concerns. There’s little chance that the Supreme Court would even hear an appeal if Congress passed these laws and Republican states challenged them.
If we change the dynamics of election politics in these relatively small ways, it will nullify voter suppression as an election strategy. That will have huge effects. At that point every politician will need to appeal to as many voters as possible. The entire primary system would be disrupted. It would dramatically reshape both the Republican and Democratic party long-term strategies and positioning. There will not be any need to take any additional, more extreme defensive steps at all.