Some of your assumptions are not quite right. You parked on private land. There is no obligation on the operator to issue PCNs that comply with PoFA. However, as the driver is unknown to them, if they want to get their money from the known keeper, they must comply fully with all the requirements of PoFA.
As we have not yet seen the Notice to Driver (NtD) and the subsequent Notice to Keeper (NtK), we cannot be sure whether they have fully complied with PoFA to hold you, the known keeper liable for the alleged sins of the unknown driver.
Whilst you have stated that they did not serve the NtK until 142 days after the original NtD, if that is actually the case, then they have not fully complied with all the requirements of PoFA and cannot hold you, the known keeper liable. The only way they could hold you liable is if, as you have already done to us, revealed yourself to also have been the driver.
This is why we always advise everyone to never reveal the identity of the driver, inadvertently or otherwise, until you’ve had advice from us and we have seen all necessary correspondence relating to the case. So, please show us the NtD and the NtK, suitably redacted but showing all dates and times.
You’ve already been advised in the previous post how to do that.