The entire post is based on hypothesis that models like "Bread and Peace" hold widely in most modern representative democracies. It would be delightful confirmation of my theory if it turned out it holds in successful ones (like Western Europe), and doesn't in unsuccessful ones (like Latin America).

As for the problems you mention. Even though president cannot run for third term, his VP or someone else from his party is likely to continue his policies, so the mechanism still works. As far as I can tell, presidential elections and national party preferences in congressional elections follow the same patterns, so if "Bread and Peace" holds for one, it should hold for the other. Incumbency preferences might weaken the signal, but as long as incumbents from successful parties have significantly higher changes than incumbents from unsuccessful parties, the mechanism works. Even if it only holds in swing districts, as long as safe districts are equally distributed between two parties.

California constitutional amendments are not really constitutional amendments in traditional sense, just a way to pass legislation by popular referendum. In theory requiring supermajority for referenda would be a source of a massive status quo bias, what would be extremely undemocratic.