Yeah, I get all of that. The assumption is that this is fixable. I suspect it isn't as easy as it sounds without a major rewrite of the database that tracks fleet carriers and sends that data to players when they enter a system. Hence my original suggestion, which will work to fix all these issues.
Will it?
It might fix the problem of having an annoyingly long list of carriers in your left panel - but would it fix the entering super cruise problem?
The entering super cruise problem would likely still exist, as you'd have to be able to toggle the filter on and off, and they are unlikely to make it so that it doesn't load anything in if you have the filter on, then loads it all when you toggle it off - that'd give a delay at a point that's not a "loading state" (super cruise transition) which is where they put these delays.
So while I agree with your idea (filer for carriers except your own in the nav panel) I don't think this would solve whatever issue is causing the super cruise transition problem.
I'm also not sure the database would need to be re-written, more, the method used to access/transmit the data, but this is entirely speculative, just seems that a data base is pretty much a database, a list of stuff - it's how you access that that would seem to be the issue here.