1) The Grox are easy to defeat.
This is what is technically known as "not true" - they are not easy. It will take a long time. By which I mean "weeks if not months of playing for hours a day"
2) The Grox only have around 600/700/1000 systems.
LIES! Well, okay, maybe... per arm and not including the middle. I'd estimate them to have closer to 7000 systems.
3) Each system will only have 1 Grox planet
I've encountered more systems with 4 or 5 planets than those with 1 or 2. I've even encountered one with 6 inhabited planets!
4) The cities can be destroyed with a single mega-bomb.
Once again, no. This is only true of the planets which are on the outskirts of their territory - I've fought cities in the centre of areas they own that took 7-8 or maybe even 10 bombs to destroy. That's because they're fully defended - filled with turrets and buildings.
5) There is only 1 city per planet.
Filthy filthy lies. Why do people who have never seen anything close to the extent of the Grox try to give advice on it? 1 city on some planets, 2 cities on most. 3 cities on one, and when that is destroyed then another planet gets 3 cities.
6) You can reach every Grox system.
Also lies - no amount of slingshotting yourself will get you to some systems, so you need to use either a mod or a trainer to get rid of your movement restriction when near the centre of the galaxy.
7) The Grox do not conquer other systems.
Oh yes they do, and that is why this has taken me so long. I was playing by the original rules at first - I worked my way out from the centre and completely eradicated one of the arms. I then moved off a bit, and came back. They once again inhabit every system at the centre, and most of the arm I had removed them from. They expand, and they do it at a rate so as to make them really annoying.
As such, here is my advice:
Get a mod to remove the range restriction at the centre of the galaxy.
Also, get the 42 mod to remove the recharge time and use limit on the Staff of Life.
The Mayflower mod is also useful.
Be a trader.
Get a good trainer - one which can alter the relations with species, and the use of weapons.
Now, work your way through one arm, to the Grox. Force them to be loyal, and ally with them.
Now they are your friends they won't attack you - won't conquer your systems (they can do that, and they can also reduce a T3 planet to be T0, hence why these mods and devices focus on increasing speed)
Buy systems, and use the Staffs to wipe them out in order to place colonies. Essentially fence them in, and then create more of a fence to cut their property apart. Cut it into small mangable chunks so you can easily set yourself targets of how much to destroy, and see if they try to expand at all.
This is how I'm doing it. It will take a long time, but it's better than taking forever, which it will have done otherwise.