maybe I mixed your screenshots troop information up and there were only 1235K Troops not 1235 Units. My glimpse was in a hyperactive phase and my game doesn´t show the strengst balance permanaently like in your screenshot. Thanks for the screenshot. Sorry if I send you an a wild goosechase.
No worries. If you were right, then I would have learned something new. There's nothing wrong with being incorrect. It's only wrong if you maintain wrong conclusions drawn on incorrect facts.
But your issue does bring up the point that there's no way of getting a count on the number of troops on a planet, especially once there are triple digits of numbers present. Hopefully it'll be added in Shadows.
1235k troop strength is rather tough. To take the planet, I think you have a few options:
1. Wait for an opportunity. The Shak are quite aggressive, and will invariably pull troops off the homeworld to invade someone. Have a fleet ready to pounce on the planet.
2. Bombardment. Soften up the planet with orbital bombardment. At the stage of the game you're likely to be in, if you sent your main fleet to bombard the planet, it would likely be reduced to a cinder in a few seconds - so you might want to consider designing and building a ship specifically for bombardment. As you wipe out the population, the defending troops will also suffer casualties. Once you've gotten them down to a manageable level, drop your troops. Be aware that there will be a reputation hit for doing this. I'm not sure if the reputation hit for genocide is modified by your relative reputations (ie: lower hit for bombarding population of a despised race as opposed to one with a high reputation) - perhaps someone who has experimented with it can chime in.
3. Brute force - invade with LOTS of troops. If you have been relatively aggressive, you should have some strength-capped troops (caps at 30k). Build troops at planets with Troop Cloning Facilities (High Tech and Industrial research, 4th in the Medical Systems branch). Move any leaders with bonuses to recruitment speed to those locations to hasten the process. And don't forget to move your strongest generals to your invasion fleet.
4. Blow it up. The Shak represent a nasty threat, so even with the loss of the wonders on the planet; so it might be worth destroying the planet with one of the "World Destroyer" type ships (assuming you have managed to grab one) if you don't think you can contain them. Keep in mind the reputation hit - and that if you bombard the planet down to "uninhabited", all the structures will remain (have a colony ship close by so that one of your erstwhile allies doesn't colonize the glowing cinder of a planet); which may make #2 the preferable option.
5. Intelligence missions - incite rebellion at planet. I've never had much luck with this option, but it's technically possible. Repeated missions to incite rebellion might be used, theoretically, whittle down the defenders with repeated uprisings. I present this option only as a theoretical. I've never had much luck with using it against a developed world.
“That which can be asserted without evidence, can be dismissed without evidence.” ― Christopher Hitchens