I have given this some thought. Where the PM is wrong is that you are not in breach of payment of rent and service charge as clearly you have, the point is doing so is arguably a waiver. As a dog is considered a continuing breach, not once and for all, payment is not a simple waiver.
There is an argument to be made for waiver by landlords X and Y who until recently were
A: happy that buyers and residents were able to have dogs
B: were at the worst not bothered about them
C: that the earlier and current PM have managed the premises and have not acted on the issue, which given the number of dogs and a normal number of visits they should be now have been aware earlier. I suspect they were, & it’s only a complaint that has sparked the issue.
The argument taken together is that they are estopped by prior agreement and acquiescence, or have in effect waived the covenant by repeatedly declining to take action in the face if evidence to the presence of dogs. There may even be a case for misrepresentation against X.
The argument of the length and complexity of the lease is fallacious, it may have worked with mobile phones and PP, and you might argue a pressured environment and the tie in with the solicitor but it won’t wash with leases, and I doubt that you would make precedent on the matter of dog. The lease is clear and you will have to reconcile that with the earlier discussion you cannot say you were not aware, you were deemed to be aware on signature. The other issue of the EU ruling of family life and pets and whether it is an unfair term to exclude completely might have some mileage, or kilometerage.
None of this is the simple definitive answer you want, any it can only be assessed by a complete review of your evidence and some disclosure of the companies X and Y and the PMs as to what they knew or were likely to know. Even then the chance of success will depend on how it falls on the day.
It seems odd that this has arisen now and one tactic is with the other dog owners to lobby the freeholder that this will cost them a lot of money, some might end up on the service charge(both depending on the leases) and that perhaps sleeping dogs should be left to lie.
There may be an underlying problem No 7’s Doberman has eaten the front door of flat 2 and toilets in the patio of No 1. No 7 might be persuaded to control their dog, but ask at a safe distance. And wear running shoes. Just in case.
Based on the information posted, I offer my thoughts.Any action you then take is your liability. While commending individual effort, there is no substitute for a thorough review of documents and facts by paid for professional advisers