Please suggest a workflow for working on a remote machine.

My organization has a very powerful machine that I use to run my ML models. It runs on some version of Ubuntu. Due to this ongoing pandemic, I have to work from home. This machine is not public facing and therefore, I VPN into my organization network using OpenFortiVPN. And then I SSH into that machine.

The problem is that my internet is not very good and/because it a mobile network that I tether on my machine (and that's why I get a dynamic IP evertime I am connected to the network). However, that machine at my organization is connected to very good network. The datasets that I work with are hundreds of GBs. I cannot download the dataset and work on my machine. The dataset and computing power reside on the remote machine, not on my machine.

Suggest a workflow for this setup. The problems I face are,

• When I SSH into the machine, I only get one terminal. I need many terminal---to edit my code for the model, to run my model, to examine datasets, etc. I don't want to exit my editor every time I want to AWK into my dataset or, run my code. The models take a lot of time to train and run, I don't want to sit and look at my cursor, I'd rather look at my code. I can finally turn to TMUX or Screen, but I want to keep them as a last resort.
• My dataset also contains images, and while examining dataset, I sometimes need GNUPLOT. SSHing into the machine doesn't give me a X.
• I tried mounting the remote machine using SSHFS to my local machine. That solves some problem, but now my local machine becomes slow due to a slow connection to the remote machine. And viewing images on that mountpoint downloads the entire directory which my network cannot support.
• Due to my choppy internet, that key press has a noticeable lag in the SSH session. As someone who doesn't even use a DE (only tiling-WMs or sometimes even without X) to work fast, this lag gets on my nerve.
• I don't know why, but if I leave my SSH terminal for too long without activity, the terminal hangs. Maybe due to bad connection, but not sure.

Please don't suggest me Jupyter (or alike) as I like to work in a terminal with my own editor (that has been vimrc-ed to hell) and also, my python scripts are dependencies everywhere that Jupyter doesn't handle well. I need my bare bones python.

Admittedly, I'm new to SSH, and VPNs and networking so, if there is something obvious that I'm missing in my setup, please tell me.