You could either get some large plant pots as previously suggested, to show this is my half, then park so your wheels are on the half. Pedantic but gets the point across.
If for whatever reason there appears to be 'bays' for parking, pull up your part of the drive and choose one of the various suggestions, my favourite being the stuff that allows grass to grow through whilst protecting from sludge etc.
You've had excellent legal advice, you need to get the rear extension sorted (plus a diagram would be lovely) you should either transfer that land to them for a cost, whether it money or the other half of this bay, your choice. You need to get into that ASAP as it's hassle you don't want down the line when for whatever reason you want a quick smooth sale. They'll take one look at the deeds, one look at the over hanging extension, imagine if this were to cost you your dream house whilst the legal wrangling a were dealt with.
You appear to be a person who doesn't like confrontation, as you've not spoke to the neighbours in 3/4 days, would it not be easier to speak with your legal team, then call EA and say just to let you know, the third bay isn't actually a bay and we'll be landscaping our 2 1/2 bays, as it were, in the near future. I just want to clear up any confusion.
Should Miss/Mrs NDN come beetroot red to your door in anger, advise you'll happily speak to the owner about it all, as there's a few more 'issues' that need rectifying as not to hold up a potential sale. It's for his benefit at the end of the day.
You've had a lot of good advice, at this point putting it off could cost you, so it's wise to deal with it ASAP. If you can't delegate it elsewhere.
Let us know how the 'friend' calling goes. It might be the Estate Agents think you can get 3 cars on the driveway, as you said, utilising the half bay and foot path, you never know.
Try not to worry how your landscaping will impact new NDN. In the first year, landscaping might be last on their to do list.
Remember as stated, you painted their house thus giving it more kerb appeal. That could be a bargaining chip if you forked out for any repointing etc. I'm sure in its old state it'd be a costly 'to do' for a potential buyer.