Firstly, I assume you are getting a train from Hayes & Harlington Heathrow as stated here:......without paying for the Tube.....
but that still leaves you a problem getting between Paddington & King's Cross, as the chances of LU staff at gatelines allowing you through are very slim indeed, and if you talk about your break of journey rights they are highly unlikely to agree that this would extend to the cross-London transfer.. I can get to Hayes and Harlington as a permitted route to London (Paddington) and buy a return ticket to Heathrow from there
I would give up on the idea of trying to use the cross-London transfer a day late and use contactless/PAYG between Paddington & King's Cross. In fact, unless there is a big time saving in going via Paddington which would likely give you an earlier connection into Newcastle, I'd consider using the Piccadilly Line tube direct (journey time 55min plus time to get to/from platforms).