It is not a case of dealing with them before they regain their strength but dealing with them before another group moves in while they are weakened and we are building up our forces.
Will the occupation be easy? No.
But it will still be easier than taking them from another group. Not to mention the fact that psionic tech might be lost to us if another group takes it and decides to sell their spoils to the Praetorians for example.
That is why I am contemplating getting some mercenary forces to increase our numbers for taking them and then work on replacing them with our own dedicated occupation forces over time to decrease costs.
Till now the New Heaven could stand as one of the big three while only fielding raiding fleets led by non-professionals. Their psionic troops never left home. From the Interlude we know that they can easily replenish any losses in vessels. Their psionic workers allow them to build at an astonishing rate and speed. I don't see any other force ready to take them on, considering their low end was enough to be considered one of the big three. Before this invasion, no one knew about the psionic soldiers, and they still did not attack New Heaven.
The Children are nominally neutral and politically motivated against playing the game with the other pirate groups. Blood is a democratic nation and how good bloody occupations go over there, everyone knows. Before trying to take land, they would use the time to focus on an easier target. Like the Sons of Teach. Additionally, I would not declare them as expansionists.
Blades are overstretched right now and face many outside forces, including a Britannian one. I don't see them focusing on taking land. They seem far more focused on loot. The same goes for Sons of Teach, first them going for a big target would break their modus operandi and secondly they have no interest in holding land and would just loot. Freelances are the same. This only leaves the Crown and I seriously doubt they will do that. Their owners would have some problems with that. Far more likely for them to pursue things with the Blades in retribution for their acts against Britannian shipping.
Furthermore, no one except us knows how depleted New Heavens pool of psionic super soldiers is. Meaning no one else knows that they just lost their major ace in the hole. For an outsider after hearing and seeing pictures of their powerful soldiers, the first reaction is not "hey let's attack that" but let's stay the fuck away. They don't know that New Heaven has lost most of their special soldiers. For all they know, New Heaven could have more hidden in their fortress cities.
I would state the exact opposite of what you are saying. It would be far easier, to break a tenuous occupation force then a fanatical one, standing with the back to the wall defending their home. Considering how doubtful I am of one pirate group being able to take even one harbor/city, I am even more doubtful of them taking all. Therefore, I do not see the chance for great loot in any way threatened. The only way that could be, if the EU gets seriously involved there and takes the harbors. But that would be a completely different kind of disaster. Such a move would be counteracted by the other big three and could easily escalate things on the world stage. Assuming a decent amount of skill in professional EU politicians makes such a course of action from the EU more than unlikely.
The Children are not Indian. They are very multicultural and their interest in India is recent. They were even raiding Indian and Indonesian shipping until recently in addition to their main target which was Chinese. They only stayed away from Britannian merchant ships according to the Pirate Dosier. Their help with the rebellion is to hurt the Federation which is their major goal.
This is nitpicking, there is obviously a big group of Indian inside the Children. Their targets from Indonesian and Indian shipping is explained away as being more targets of opportunity than deliberate acts. That is a difference, an important one. Then how do you know their interest in India is recent? I would say they always had an interest in India considering they most likely have major backers from there. It is the best explanation for their parity with Federation technology. Their infiltration of the upper echelons is recent, but that is a little bit more than interest.
Currently, there is a major faction inside the Children, including Rakshata, that is interested or has the goal of Indian Independence and some of their biggest backers are from India.
Jack is more about encouraging independence and nationalism in some of it's larger member states by showcasing their powerlessness.
Yes, the Children want to hurt the Federation, but they are not bloodthirsty edgelords that just want to see the world burn. Jack obviously has an interest in the independence of India or all states inside the Federation.
I don't think the obviously influential group of Indians inside the Children and the overall group would be okay with jumpstarting a rebellion, that is doomed to failure, just for fucks sake. You can only hurt the Federation by showing them as weak. Them easily crushing a rebellion, showcases the exact opposite.