May 26 is a public holiday. It is affecting the trains to Manchester in that no services can run on the direct route due to engineering work (they are being diverted via Birmingham with an extended journey time).
Also no services are running to Scotland via Preston due to separate engineering work so are further diverted non stop via Manchester.
I don't understand that you have both Brit-rail and Two Together. You don't need both as Britrail covers all trains, and there is no further Two Together Discount for Britrail.
Assuming you are travelling with Britrail you don't need tickets and just take whatever is the next train when you get to Euston.
If you are needing a ticket (not travelling on Britrail) Advance train specific tickets are on sale now starting at £43.50 (before railcard discounts). But yes it would be a total guesstimate against the flight being retimed/delayed/or even running early as eastbound TA's often do.
Far better to buy an Off Peak Single for £79.80 each (before railcard discounts) which is valid on any train on a walk up basis.
Buy on the Avanti website. Split saver ticketing is utterly crazy when travelling into the unknown like this. In any case the usual split fare hack on Advance Fares which gets you to Manchester from London for £10 after railcard discount doesn't work with the diversions.
The other usual split fare hack of St Pancras to Sheffield to Manchester is working that day (about £18 that way after discounts with careful choice of train) but is similarly not adviseable.
I can see a split fare offer that day on two Advance Tickets of a 5 minute change at Stafford which feels like loony tunes to me.
In theory with everything in your favour time from landing to Euston should be two hours. The Piccadilly Line tube route is closed that day from Hammersmith through central London to Cockfosters- so you are on Heathrow Express or the Elizabeth Line changing en route for Euston.
The fastest and cheapest route is Heathrow Express (Early Bird Tickets for £6.65 to Paddington available with your railcard + the tube fare of £2.80)