Another tunneling question

Well, I am in an university hospital environment. Our research group is working with a couple of people on building machine learning classifiers to aid patient diagnostics. For this we have a linux machine equipped with a powerful GPU. The researchers who used the linux machine logged into it using thinlinc from their windows clients, which worked beautifully! However, recently the hospital networking rules changed and the linux machine received a strict ACL requiring everyone to log onto the machine via a jump server, which requires hospital login credentials.

I was trying to figure out how we could keep access simple and straightforward for the client. With the fairly simple ssh config above it works well with the ssh plugin for VS Code on the client side.

So now, I am trying to figure out if I can change the thinlinc client configs for our researchers to regain access again before having to tinker with the jump server itself. But I guess the most straightforward solution would be the latter.