To be more helpful to the OP, the place you are at the moment is adversarial conflict - no-one is talking about their needs, both of you are going into firing solutions back and forth, which each is rejecting in favour of their solution - in effect you are in a negotiation, and that negotiation has reached stalemate. Probably because even if you see yourself as 'budging' you are intending to hide your compromise position within a list of demands.
From the other party's POV, you have both come to an agreement (one day a week) perhaps in a way that meant he didn't want to, but we shouldn't speculate. We don't know completely why his position has changed, but at least at the moment he feels unable to look after them one day every week.
We also don't know why the payments dropped, but they did. This could be because he resents paying and not seeing children, it could be because it is a drain on his finances he feels he can't afford, it could be because this stretched connection to you is troubling him at the moment and preventing him from moving on.
Whatever it is, that act would be need to be investigated, and the real need understood. Assuming it is a power tactic, then responding with a power tactic will get you into more conflict - as your reporting to CSA demonstrates, this will then result in a reactive power tactic 'you've shot yourself in the foot' etc - Strong power tactics will erode goodwill inthe negotiation and should only really be used if you want no future relationship at all. I suspect if you are honest with yourselves, probably at those times of rage that is what you want and the horrible responsibility of having to remain connected is what is causing all the stress.
Not only that, but staying in conflict mode (as in adversarial conflict mode) will become all consuming - in this case becausee of the children, there will never be an all-out winner on each side. This needs to be understood at depth by all participants, and a good mediator will stress that there needs to be at least some relationship continuing - at the moment that continuing relationships is as damaging as it could be, and you should seek to work towards one that isn't.
If your partner is a real power buffoon, then frame the arguments for his needs in terms of power and money - don't assume this, as you can be surprised what the real reasons are - eg 'If we find a way of managing this that is flexible and agreed then you can forget about it as a problem and just get into a positive routine' or 'neither of us need to be working against each other when we could instead be focussing on our careers, on having the best days with the children and finding ourselves again;.
Its easy to get angry, and a lot of posters here are also projecting their own anger about their relationships on to you. Mediation can work well, but even if you don't use it formally, try to understand where you are in the conflict process - resources such as 'ladder of inferences' (look online) will help you understand what both of you are doing - it is worth also reading some literature on negotiations and what you need to do to prepare if the other party carries on in fight mode when you are in resolution.
Keep aware that you MUST keep a relationship between you and this will necessarily hold one or both of you back from full nuclear actions (hopefully). In a negotiation nuclear options are rarely used, but threatened often - most usually by the party that is feeling weakest.
I would suspect here that he is feeling that you have control over the childen, and therefore he resents paying 'for nothing', but you see his power in the money and other tactics, and so you are waiving the CSA as your 'nuclear' option. All this behaviour is unhelpful to a lasting resolution as each of you will be evaluating 'how much did I take from them' or 'how much did I give away' - and that will lead you to continue being in the conflict after it has seemingly ended.
Worse, if there is a genuine power imbalance, playing your strongest card against one that is stronger, means that normally it would be game over.. but then you are back to the enforced continuation of the relationship.. and back into playing the game. The children don't need their parents locked into a constant power game - they need support and help in making the most of their lives.