The crossover between crusade guys and zionists is kind of interesting in a way. You'd think they would aim to make it a christian state again, but maybe that is stage 2 of the plan.
It is actually worse than that, they want all the Jews back in the holy land to fulfill their apocalyptic death cult bible fanfic. After the final battle all the "good ones" will repent and become christian and the rest will be murdered by burger Jesus as all the most burger worshiping "christians" get taken up to heaven where they will have unlimited fountain drinks, McRibs and hooters girls serving them, not unlike their caricature of what they believe about Muslims and the 40 virgins bullshit.
He has a Kingdom of Jerusalem tattoo and a load of crusader stuff on him though, which is a different flavour to the other evangelicals at least in my experience. But maybe that is just outside of the US.
You are giving him too much credit (i.e., assuming he has a well thought-out coherent connection to those symbols instead of the being vibes based history). The original crusaders were Catholics, which Pete is not. The current Crusade is a Protestant Crusade and he sees himself as a Protestant Crusader (notwithstanding the catholic imagery he got permanently etched into his skin). The Protestant crusade is along the lines of what Nakoichi laid out - they conscript Jewish foot soldiers as functionaries within their Protestant theology to crusade the holy land for the protestant end-times which requires "Jewish" control of the land.
My point is that he doesn't have any serious belief in anything that you're describing, just that he is incredibly racist. They also tend to hate jews, only slightly less than muslims.
Trying to see it through scripture at all is already giving him too much credit.
I think you are correct that if they aren't in the camp mentioned by Nakoichi, they are in the camp of "getting all our enemies together in a single ethnostates makes them easier to conquer"