Hey Colin,
So Jupyter does support something like this. It has a client-server model where jobs can be farmed out to separate remote computers, but I've never set it up. I also use qiime on a supercomputer and here is what I have found works well for me:
Instead of spinning up the notebook server on my laptop, I spin up the notebook server on the head node of the supercomputer, then use my laptop to access this remote server using it's IP address and Jupyter notebook port. So while I've viewing and editing scripts from the web browser of my laptop, the scripts are living and running on the remote supercomputer.
Does that sound like it may work for you? You can install a Jupyter server using miniconda (no sudo needed) if you want to give this a shot.
The qiime devs use Jupyter more than I do. Maybe they have some advice.
Colin