Perhaps the gas giant and zero level planets could act as "Easter Eggs" in the game - another form of Space anomaly. For example, you know how in the game where if you accidentally send a colony ship to a planet that requires a terraforming technology you dont have yet, and it pops up a message something like: "You need to research Barren World Colonization to colonize this planet"?
Well, maybe if you do this against a zero level planet, it instead randomly pops up a dialog with an "Easter Egg prize". The thing is, you would actually have to select the planet in question and send your ship there - it would not occur simply by scouting the region - the ship has to actually target the planet as a destination.
Once a ship reached the destination, there would be a random determination if there was some special "prize" or action associated with the planet. Some examples would be:
1) You find crashed remains of a ship floating in orbit around the gas giant. Inside the ship you find XXXXXX.
2) You discover the remains of some long lost precursor device. When you mess with it, it implodes the planet - taking your ship along with it. OOPS.
3) You discover a device that transforms the planet into a Level 2 planet. Ugh, but maybe the 2 tiles have special bonuses. At worst, you have a couple of farm worlds for another couple of billion people...
4) You discover some unknown alien race's long abandoned ship in the outer layers of the gas world. It is definitely a combat ship of some type, and might be a worthy addition to your fleet...
5) The Gas giant contains the right mix of gases and materials that can act as fuel for your starships - so now your range is extended for an additional extra number of parsecs in this quadrant...
6) Nothing special about this gas giant. Just another Gas Giant among millions. Thanks for playing, go home now, no consolation prize...
You get the idea. There would only be one Easter egg per gas giant planet. Once claimed, the gas giant might take on a color tinge that would indicate which race got to it first. The thing is, you would not see the tinge until you actually got to the world. SO you would be forced to go to every world during the game to see if all the Easter Eggs had been claimed or not. This would actually give your survey ships something to survey besides space anomalies. If you found a planet that somehow got terraformed as its Easter Egg, you would be the only one that knew it was terraformed until another race actually got to it. In that circumstance, once they make contact with the planet, then and only then are they aware it is habitable, so this gives you a chance to get your colony ship to that planet first before another race discovers it.