Good,
Surely all the mess on the WCML will be over by then.
Corbridge to Newcastle just turn up at the station and buy from the automatic machine. There are no advance discounts and no reserved seats so no point to buying in advance. It's £7.10.
Once (if) the engineering work ends on 4 June start looking at the Avanti West Coast website and try to establish what is happening then.
https://www.avantiwestcoast.co.uk/travel-information/
This web page is the most up to date data on Avanti.
If you are still struggling in late June come back here, and we'll see what is happening then.
Who knows, Avanti are on warning, they may not have the contract by then, it may have become an essentially nationalised company, like LNER on the east coast.
At weekends new engineering work keeps being added at 2 weeks or less notice, presently.
Check that web page each week and see what is being released, but the maximum release date is about 6 weeks beforehand, currently. One big tip is that Avanti are not being honest on this web page and haven't been for months. Once tickets are released for dates about 2 weeks before your travel date, click on the 'Buy Tickets' button on that page. Very often advance tickets are being slipped out quietly before Avanti admit on their own web page that they are out. You should get an Edinburgh to Carlisle advance ticket for £9.
Transpennine Express operate alternate trains on the route, but their fares will also appear on the Avanti website and are usually being released on the same kind of time frame, slightly more expensive.