If you don't want to use the palace jump don't use it.
Ultimately, yeah, you're probably right. I consider it cheating, but if you want to do it in your single-player games, I say, go right on ahead. In MP games, I think I'd be pretty angry if someone used it, but then, I almost never play MP games.
I also realize that CivIII is not a historical suimulation.
That said, I think it is a rather glaring exploit (read, cheat) for someone, through their knowledge of the inner workings of the game engine, to rush-improve and rush-populate a city far from their capital in order to slingshot their capital half-way around the world and gain an advantage on either the AI or a human opponent. Firaxis has addressed less egregious exploits than this one (RCP, for example).
But I still would like to know what this "code change" will do to the legit palace jumps.
I'm not sure what you mean by legit palace jumps. I think by simply implementing idea #1, you eliminate almost all exploitative palace jumps, and don't really change the balance of the game, except that now you do not have access to a technique that is never used by the AI. That way, if you want to move your palace, you can either build a new one, or rush-build a palace with a GL.
I do not want to be on the losing end of a war, lose my capital and then lose the ability to produce new units to defend the rest of my civ
Yet there is some historical precedence for this. Paris fell in WWII, and France immediately sued for peace. Even a 1-2 turn period of anarchy and upheaval seems reasonable while your gov't regroups.