I'm not sure if it would work with self employed ex but when my ex got a promotion and foolishly posted it all over fb (which he knew I could still see at this point) he was paid in cash (but I doubted was cash in hand) by his employer, I was also frustrated by cms inaction at first so I contacted hmrc to ensure they knew he'd had a pay rise. I was right that he/his employer were keeping right with hmrc but ex still hadn't told cms
Cms were contacted by hmrc and an increase in maintenance and back payment supposedly organised
That said he also "played the system" and rarely paid on time/regularly/in full he would only pay when the csa (as was) started threatening an attachment on earnings and then he'd pay at least a nominal amount which got csa to back off.
Dd was 15 when cms came in and we were transferred and I raised all this with the case handler and he did seem more on the ball and got an attachment of earnings based on the pattern of my ex's behaviour inc arrears
Then dd decided to drop out of school at 16 and go to work (not entirely her fault school were being arses too) which meant no longer eligible for cm
But the arrears also weren't pursued despite many calls etc to cms and even my Mp chasing with them they just didn't want to know.
So I would urge you to do all you can be a total pain in the arse to them before your child leaves school and becomes ineligible for cm as when that happens they basically just wash their hands of the whole matter!
My ex's arrears were over £10k
Cms aren't fit for purpose we need cm back where it belongs being dealt with by the courts because it's not something where "one size fits all" and algorithms for calculations can ever work.
There are so many variations in nrps who exploit the loopholes - Job hoppers, self employed, going overseas (either emigrating or going "home" to country of origin), taking the attitude that children are "pay per view" etc
There are also (whisper it we're on mn) mothers who don't play fair too - claim from more than one nrp for the same child (how are cms not tracking this?!), accept cm in cash and then tell cms nrp hasn't paid, also treat children as pay per view
But I will say that by far the nrps tend to be the ones that most often behave badly - whether men or women I happen to know several single fathers with Mother nrps and those female nrps have behaved exactly as so many male nrps do.
If it were dealt with on a case by case basis I've found family court judges are generally pretty good at getting the measure of those involved and the situation and I think would for the most part act fairly
There's also the question of the current levels/calculation of cm is in most cases a pittance! It certainly usually isn't equivalent to 50% of the cost of raising that child as it should be. Or even 40%!
It's a mess all of it
I hope you manage to get a solution op