Any strategies or tips for getting the tutorial slots I want?
Not much for the first round as it involves only ranking your choices without any information on the current number of balloters. In the later rounds where you are allowed to add/drop your assigned tutorial slot or request Swap slots, do it as early as possible. This means, do it at the time the round opens. This strongly increases your chances to get the desired slot or to get the first slot in the queue for swapping.