I think the FA Cup final is key - as long as Utd win it won't matter if City or Utd finish 5th in the Prem, either will have qualified for the Europa by way of a cup win, and the second EL qualification place, released by the 4th placed team gaining an ECL slot, slips to the 6th placed team. This, I think, caters for consequences of Liverpool winning the Europa League, and thereby going into the ECL - leaving England with 5 ECL and 2 EL qualifiers.
IMO, the midweek games need to produce a Man Utd win and a Liverpool draw ( or defeat ).
In that situation, provided we beat Palace, I reckon the Premier League table & consequent European places would be;
1) Leics - ECL group stage
2) Spuds - ECL group stage
3) Arse - ECL group stage
4) Man ( Utd or City ) - ECL playoff round
5) Man ( Utd or City ) - EL playoff round
6) Saints - EL 3rd qualifying round
7th or 8th ) L'pool - ECL playoff round
7th or 8th ) WHU - nowhere