A formal police caution is only given where there has been an admission of guilt and if your exh and his new partner are formally cautioned by the police this will be a vindication of sorts for you.
The majority of claims for libel, slander, and malicious falsehood are settled out of court and, unless your exh is famous or exceptionally wealthy, any such claim you make is unlikely to attract the attention of the press and result in the 'public righting of wrongs' you desire.
If your exh is cautioned in connection with an offence he has committed against you I would suggest that you publicise this fact by verbally informing your boss(es), colleagues, and as many others as possible while ensuring that you firmly adhere to the facts of the matter and resist any temptation to add extraneous detail.
Unless it has been approved by a solicitor, I strongly advise you against putting anything related to the matter in writing as you may unwittingly cross the line between fair and unjust commment.
Regardless of whether your exh and his new partner are cautioned by the police, I suggest you give consideration to instructing a solicitor to solicit an apology and an assurance that they will desist from defaming your good name and reputation.
However, that said, I personally would not be inclined to spend money that could be used for more pleasurable pursuits on this pair of bare faced liars and would rely on my professional reputation and those who know the true story to refute their false allegations without cost to myself.
Fwiw, there's no reason why you shouldn't go round the streets with a loudhailer proclaiming his failure to pay maintenance but, before doing so, you're best advised to give thought to how raising public awareness of his reluctance to provide for his dc may affect them.
I hope that next month's court hearing results in a stunning result satisfactory outcome for you and also hope that you'll come back with an update as to whether or not the dastardly duo are cautioned.