For tests and exams it’s common for teaching assistants to mark the same few questions on every test, usually on the same page. It helps catch cheating and plagiarism and keeps grading consistent.
When I was a TA we’d split the stack of paper tests evenly and rotate them every few days to grade them in parallel. It’s even easier to do the splitting if tests are submitted online.
Oh, yeah! My profs'd also post the list of which TA did each (sub-)question, so that if we had questions about why we lost marks we knew who direct them to (although all grading disputes had to go to the prof, to disincentivise people from arguing with the TAs)
And with two teachers, you'd also be able to have each write half the questions, and split the grading that way.
When I was a TA we’d split the stack of paper tests evenly and rotate them every few days to grade them in parallel. It’s even easier to do the splitting if tests are submitted online.