In terms of mapping, unless you extremely unlucky, you can use the matryoshka approach.
Basically, long connections run around and inside you have the rest of the systems, if you use a squared map system.
If you use a spiral approach, you should then be able to keep the same approach by dragging the connections on the out arms and spiral inwards.
Skoormit, out of curiosity can you send your DB? I would like to have some fun with your map. I am asking because I never really encountered a really messy run in terms of inter system connections. I guess I have been lucky (or unlucky, depending on point of view) so far. It is true I only play with Real Stars map, and I noticed that this situations are most common in non Real System starts or if you mess around local systems connections.
Steve, in your case you only need to switch the position of Tannauser gate on North West side and move Kodiak up of Andromeda.
Once you done that, you should be able to quickly figure out the best position for Barbarossa and Dark Heaven to pass on the west side of Sol while keeping Paragon and Argonar in the right place, as they don't need to intersect. Proxima connection can be placed anywhere free and out of the way at this point.
I'll admit that Regulus will require some creativity. To be fair, create space for that part of the galaxy should be doable until a new connection turns the table. I think you'll have to skew the whole map to the south west side until you can squeeze the last intersection through Lethe, considering Alpha Centauri should be already in an ideal position due to the previous Barbarossa move.
If I may, this presents the perfect opportunity for me to brainstorm on a couple of ideas. If you ever played Avorion (please don't or Aurora will get put aside for too long
) I like the warp concept there, so basically the map does have these long warp points from one end to another of the galaxy. If we can have some means to "rearrange" selected branches to pass on top of systems circles or elements and not underneath, then this will already be a possibility (it will require for them to be of a darker/lighter colour though). I do know there is something going on there, because I noticed that intersection pass over other intersections with a discovery priority? Basically, they do not exist in the same layer. You can notice that when you build gates and the line becomes orange, and by using Skoormit map it becomes evident. Some goes on top some others below. Perhaps there may be space for layer optimization here as well, helping with performance opening large maps. Am I correct? If not scrap it.
Eventually, the branch could have a selection and a toggle called long connection, which will make that particular branch of a different colour if selected. I don't know, perhaps red and pink if gate connected.
While at it, and I know it is a pain, Zoom and grid size selection features back will be highly appreciated
There is always the good old don't touch it if not broken approach.