I'd say Lancs v Essex is the hardest QF to call, unless the ECB allow Lancs to be at full strength. But that's incredibly unlikely to happen.
Brook, Root, Bairstow, Willey, Malan.
Jordan, Roy, S Curran, Foakes, Pope, Topley.
Livingstone, Buttler, Parkinson, Gleeson, Salt
C Overton
Tuesday: last day of test match
Wednesday: Surrey v Yorks
Thursday: England v India t20 & Birm v Hants
Friday: Lancs v Essex
Saturday: England v India t20 & Somerset v Derby
Root, Bairstow and Overton are all only in the ODI squad - and Pope and Foakes aren't in either squad. But will the ECB let any of the four test players appear, just a day after the test match? My guess is that only Overton of those five non-t20 players will be available.
There's also the start of the Ireland v NZ series on Sunday. Stirling and Allen are both affected by that I think. But given that they're scheduled to play on Wednesday and Thursday respectively, and Dublin is hardly the other side of the world, I presume both will be available.