Hi Ealinger,
Firstly apologies for the delays in answering. I’m not quite sure how I missed it. Taking you questions in turn:
According to Google maps it is about 800m between Belsize Park and Hampstead Heath. There are very few OSIs at that distance or more, ignoring some odd NR-NR ones like Paddington to Marylebone that hardly anyone uses. However, one that is also 800m is Leytonstone to Leytonstone High Road. It might be worth asking TfL if they’d consider adding the Hampstead one, though I think they might say the closer Camden interchange would be more popular.
None of the routes are particularly attractive given the need for walking between stations, so I guess they think you might go via Blackhorse Road. Again, you could ask them.
The best way to contact TfL about these issues is via the Help and Contact page on their website, selecting the Tube/Overground/DLR etc option under enquiries.
I believe that the issue with changing at Blackfriars has been resolved by providing a credit if the system detects that you’ve used TfL priced fares only. I certainly tried that one recently and did get a refund automatically. It is likely that contactless will charge correctly in that instance.
Where contactless won’t charge differently is if there is no specific route defined, so your via zone 1 default fare will still be charged via zone 1 unless a defined avoiding zone 1 route is used.