What your tenant is misguidedly referring to is the part payment of overdue rent which will negate a section 8 claim for eviction on the grounds of unpaid rent.
There is no such option or recourse in regard to your right to register a CCJ. If they owe you money, the actual portion of the rent paid is irrelevant once you have lodged your claim, except of course the debt due will have been reduced accordingly.
However, I believe the same criteria of a minimum of 2 months rent being outstanding at the time you claim is required. That is one full month plus the day the rent becomes due for the second months rent, not 2 whole months.
If you are seeking to evict the tenant as well as claiming back your losses, you need to apply to issue a section 8. If you are seeking an eviction on unpaid rent grounds without requiring repayment of the debt, you need to issue a section 21.
Regarding the contents damaged / stolen, the tenant is liable for those costs against their deposit and, if necessary, a county court claim, which can either be in the form of a section 8, as described above, or a simple county court claim for damages, in addition to the unpaid rent on one combined claim.
A County Court claim can be registered relatively cheaply online then, if there is no response to your claim, you can apply online for the court to register the CCJ against the defendant after 2 weeks. If the defendant rejects your claim, you will have to request a court hearing for a judge to decide the outcome.
Make sure you include the wording on your claim that “you require the court to grant the release of the DPS deposit #…, in the name(s)…, at the address… to you”, to ensure DPS cannot withhold the deposit.
I cannot be certain, but I’m fairly sure the police will not get involved, stating it is a civil not a criminal matter in respect of your tenancy agreement.
Aside from all the alternative recourses, whether or not you get recompense depends on the integrity / ability of the defendant to pay whatever you are awarded. You do have the further option of requesting a warrant against their assets if they refuse to pay the court awarded sum to you.
If you issue a claim through the Small Claims Court procedure, you still cannot apply Court costs to the defendant if the case is found in your favour. Yes, I know, it’s very unfair that you are subjected to those costs when it is your only course of action to recoup your losses.
If you have sufficient funds held in deposit, in particular the DPS, you can make a claim through them for the release of the funds to you. If the tenant objects you can request it be settled in DPS’ arbitration
process for free, but only if the tenant agrees also to this process, otherwise it has to be a court claim. Beware, the DPS are renowned for favouring the tenant in such arbitration awards, so make sure all your evidence is watertight.
I hope this helps and that you get a satisfactory solution eventually.