Thank you for your reply. I minibatched all the related variables together and that seems to have fixed my problem. I find it odd though, because based on what I saw here: How to make Minibatch for multi-dimensional data? - #4 by ckrapu It seems like it was supposed to be faster to set them all separately. Granted, that was 4 years ago.
The reason I was using replacements is because when I would like to be able to use the pm.set_data function later to sample using new data, and it didn’t appear that was possible if I directly used the minibatched data in my likelihood function.