[clarnibass]

I have done that very thing, to lengthen a rod (brass). Though I didn't do it with swaging pliers. I just gently peened the rod against the anvil of a vise, working my way round and round the rod, till it reached the desired length. Easy peasy.

Yes definitely possible, this is the "no special tools" method. There are some special tools made for this specifically. I have the Ferree's one (which works but I don't particularly like it) and the Boehm one which basically works the same as what turf3 described, but with close matching contour around the rod.

Well, if you were to lengthen that C# rod by some heavy swaging in the middle of its length, you wouldn't have to fool with either post; you'd reduce the misalignment at the north end; and the horn could always be returned to original configuration very easily.

I'd suggest that the misalignment of the keys won't be noticed in actual play, but if it is, one could solder a 4 -5 mm extension onto the end of the C# to make it even. (You have to leave a hole for the roller's screw.) We're not talking about high collector value horns here; just modify as needed.

Yes I guess it depends how much it is felt when playing and how accurate whoever has it done wants them to be.

The photo doesn't look like it, but going with JayeLID's post of a 6mm difference, so 5mm if it's touching the upper post (I tried to find a translation... there doesn't seem to be a good word for this in English), I guess the question is how close you want it.
It could probably be adjusted closer by slightly curving the C# and maybe minor S bends in the B and Bb, which might be good enough for the OP, or not.
There's the issue of the rollers being apart and there's the problem of the gap between G# and C#. An extension to the C# touchpiece is definitely an option and it will solve the latter but not the former (assuming it's just an extension at the top... the touchpiece could be modified more).

I've seen some DIY brass sculpting that was pretty good, but the main reason I suggest having a pro do the work is that (IMO, at a minimum) you should hard solder (silver solder) any extension additions, and silver soldering is more complicated, and better left to someone with experience with it, than soft soldering.

IMO no pro is going to tell you to soft-solder that, unless they don't give a **** what other pro's think of them or will say about them.

I guess the question is what is "that".
If someone is going to put a significant extension, let's say about 5mm (going with JayeLID's measurement), on a hinge rod (solid), with this extension area being the one that is supporting the hinge against the screw, then yes I'd want to braze it (hard silver solder). So in this case, sure.
If it's a small extension, say about 1mm in this case (if not moving the posts), it will make no difference to the support since most of the contact is not at that very short end (I would want to verify that, or fix it if that's the case), then I would probably use soft silver solder (silver bearing solder).
Even more so on a hinge tube where it would make no difference and especially with lacquered keys (which isn't the case here).
Just to add that it's more about the exact details rather than a general idea that key extensions need to be brazed.