I can only share with you how I handled this - no idea if it is right and I imagine there is more then one 'right'
I live in the US so some of the legalities will surely be different too. Also - we have joint legal custody, I don't have sole custody - so also different.
We were both told (by our individual atty's) that the judge would not sign off on the divorce without having child support set. We didn't question this so I don't know if an exception would have been granted or not. There is a formula they use here to determine minimum child support payments and since he was not working at all - they plugged in a full time minimum wage income for him.
If I turn this over to social services - they find him as long as he lives in this state and is working legally (ie not taking cash under the table). If he moves out, then all bets are off. If he is in arrears it also causes some issues for him - and I think his tax return is sent directly to me.
I felt a lot like you did at first - and I also didn't want to kick him when he was down so to speak. After some thought, and speaking with my counselor, I changed my mind. This is not $$ for me, or to make my life easy, or to punish him, or demand that he be accountable. It is money for the kids. They deserve this money. I am cheating them if I decline it. I can feed them but there is a lot that I can't provide for them. So when I looked at it from that perspective, it felt like the right thing to do in my case. It felt like putting them first. I also totally just lost the 'kick him when down' worry. That was codie and putting him above the kids. Ugh, makes me sick to even know that thought went through my head.
Best of luck in your decision. It seems like so much is riding on this, since it isn't all final yet, and I totally get that. I made a lot of concessions with my divorce - they were based out of fear and just a desire to be done with it. My counselor helped give me some strength to 'un-concede' to some of them and others I conceded. Some of it I have a smidge or regret over and others - not so much. Some concessions are worth it. I don't like to gamble
Oh, and as far as the worry over the other 'players'. I think you just need to take that off the table. You can take care of you and yours. That is your responsibility. They will do the same on their side.