OP, in all honesty this is getting overly complicated IMO.
First of all, a lease is a tenancy agreement it's just that when it's month to month or short-term occupation the term tenancy is used, but when it's longer the term lease is used. There are other distinctions one of which is referred to in one of your posts in which you show the assignment agreement! This is necessary because although you can dispose of your lease, the freeholder needs to know that the assignee (buyer) obligates themselves to covenants just as the tenant(seller) did.
It is clear from what you've posted that the Mgmt Co's ability to make 'regulations' or otherwise place limits on occupiers' freedoms is circumscribed by these being only in respect of common areas, buildings and grounds, NOT occupiers' property per se. They may place limits on HOW your property is used e.g. no hanging of washing out of windows, no nuisance, no fires etc. (I wrote this before reading the Tenancy Agreement, so a pretty good guess on my part!) but IMO these would be either specified or referred to in your occupancy agreement which in your case we believe is a lease.
I think your draft strays from the centre-line.
But before you send anything, where is the mgmt co's email refusing your 'opt-out'? With respect, and I think you've touched on this yourself, you are not adept at compiling such communications and I suspect that there's been miscommunication with the Mgmt Co. Their role is prescribed and circumscribed by their Memorandum and Articles - see the manual and you'll find this stated clearly. They are a legal entity, they cannot simply invent rules.
Dear Sir,
Re: ***************
On ** and **** my vehicle, VRM ****, was issued with Parking Charge Notices presumably issued by your staff. These purport to claim that the driver is indebted to you for a parking charge for which they are liable by virtue of them breaching a contract. The contract in question being one which you believe all drivers who park in the **** area enter into with yourselves. In the case of these PCNs the breach was ....
and when I got this far I had to stop because the PCNs in your posts don't include the alleged breach!
Neither have you actually contacted them so you don't know whether they would without argument accept they've made a mistake, so I think your first letter should adopt a tone which accepts that this is just a mistake.
So:
The alleged breach(es) pl.
The Mgmt Co's email, pl.