The IAS upholds 4% of the appeals it receives, and I have never seen it uphold one on rights to park in allocated parking spaces under a lease.
If your lease esentially gives you unfettered right to park, a parking company can’t impose terms on something you already have a right to do. The “breach of the displayed terms” is nonsense.
You can display a permit as a convenience to you if you want, but it’s not a requirement.
The IAS is supposed to be operated by people with legal training, but we have never seen any evidence of that and doubt it very much.
In the absence of any help from management, you should assume you will receive a Letter of Claim followed by a county court claim. Most court claims get discontinued as long as they are properly defended, and you seem to have the basis for a proper defence.
I suggest you search the forum for similar cases, brought by UKCPM or others. I don’t recall any of them that are fully documented (ie that are documented to completion) going in favour of the claimant.