Anyone ever use an SSH Bastion/Pass-Through to minimize Application Connection Jitter?

So, I've been dealing with a problem for a bit now, and I had an idea this morning that I don't know if it'll work.

Scenario:

I have an old-ass application running via SSH. Like, there's some potential green display screens are used. The moment that this old-ass application hits any spike in Network Jitter, it'll close the connection. It is very sensitive. Now, the obvious answer is, of course, the monster of QoS and prioritizing the traffic.

However, I don't have any existing QoS policies setup, and it would take a substantial effort to build a decent QoS policy on my MPLS backbone. I'm not against it, and I think its the best plan in the long-term, however, I have global priorities and deployments to work through....So, I'm trying to take a quick short-term route that might be beneficial, and I was curious if any of you had deployed anything similar.

So the idea is, what if I stood up an SSH bastion at the local site? So, the clients SSH to their local server, the local server establishes an SSH connection up to the remote databases, and in theory the connection wouldn't just as susceptible to the Jitter, because the client is just connecting to a local host, versus client to far-off-in-another-place.

I mean, yes, in theory the total amount of latency and Jitter is the same, it's just the idea of trying to trick an application to not be dumb, because I'm trying to make it think it's only talking to something in it's LAN, versus across the WAN.

I know it's a stretch, and because I don't really know how the old-ass application does it's connection handling, it might be all for naught. So, I figure before I spend any cycles on anything, see if anyone else has done anything as similar or as dumb, or been involved with our SysAdmin counterparts as such?