we faced a somewhat similar dilemma since we had tickets the day after a strike and there were articles that said trains would be out of position and even on the 1st post-strike day some runs would be cancelled. As a backup plan we bought bus tickets thru National Express. We bought them a bit farther in advance and they were only around £22 on National Express.
While I'm by no means a transport expert, you might want to buy the bus tickets for around 2 hours after your train departure (assuming you have a departure time around 9am or earlier). This gives you time to try and take the train, then get across town to the Victoria bus station. Personally I'd just figure LNER isn't going to run and try to take an early bus so we still get the afternoon in York.
The price of the tickets may rise as the date nears and possibly sell out; there are only so many bus seats to York. I'd be willing to buy the tickets now even if hoping we don't use them; I figure it's better than not getting to York until the next day, having to pay for another nite in a London hotel while also paying for the York hotel, etc. Others may choose to take the risk.