I wouldn't describe in such harsh words (although maybe that helps bring the point across?), but overall I agree. Several of the items look like they could be improved completely isolated from the rest (eg. the email issue).
Moving from Wordpress to Laravel means that the basic stack remains the same (PHP). All in all, this looks like something that ought to be possible without a rewrite.
I'd start with building a new front router that calls liberally into wordpress as a backend.
Once wordpress is only managed (and accessible!) by the front router, one by one hack up wordpress to call into Laravel Spark stuff (eg. the user database) instead of using its own infrastructure. The end result would be that there's no wordpress code being used anymore (so drop it), and the site is completely moved over.
But that way every step in between won't be a regression to users, and it's realistic to add the odd emergency feature addition to the platform without having to maintain it twice (in the old platform and the new).