Here is a gameplay variant I've played with extensively and loved.

Players add their home system into their hand of systems and can play it on any of their turns where ever they want to. The only placement restriction is you cannot place next to another home system.

I have found that under this system, players start closer, so fights start early and continue for the whole game. It increases the chance of players being eliminated early. My group has largely adapted to that risk by becoming really paranoid and always keeping 4+ ground forces in their home system even if it looks safe. Especially in games with 4 or more players, there often are one or two players who get stuck with two opponents within two hexes. But this is effectively a result of losing at deployment. The system gives you a lot more control of your initial surroundings, but poor starting locations are a bit more common.

It's very hard to turtle under this system. Players who can sit back and build up there forces can only do so because they've kicked the crap out of everyone nearby, or they've chosen an isolated, and likely resource poor area of the galaxy that nobody wants to invade.

What do people think of this variant?

We play a varient very similar to this where we put our home systems into the "pot" with the other systems and are all placed randomly. Proves to provide some very interesting games when your home system is only one grid away from another players.

This is a cool variant that has been invented and used by many people over the world

At the Twilight Imperium 3 wiki forums there are many ongoing play-by-forum games and some of them are using this variant. There it is called the Star-by-Star variant.

The wiki community has also created several preset maps using setups where the home systems are not in their "official" positions, but rather placed more freely on the board. Check this link!

We normally create the whole galaxy randomly, including the home planets. Makes for much more fun...