I said this in the snap poll thread, but the next 7 days will be a good indicator of what happens IMO. After that, Leeds and Leicester have significantly harder final 4 games than Everton.
Leeds: @ Man City, Newcastle, @ West Ham, Tottenham (#2*, #3, #13, #5 in the current table); West Ham would be 3 days after their ECL semifinal 2nd leg
Leicester: @ Fulham, Liverpool, @ Newcastle, West Ham (#9, #7, #3, #13 in the current table)
Everton: @ Brighton, Man City, @ Wolves, Bournemouth (#8*, #2*, #14, #15 in the current table); Man City would be right between their 2 CL legs with Real Madrid
*Brighton and Man City have played significantly fewer games than most of the League (29 and 30 respectively), so their position on the table might be misleading
If Everton is within a point of Leeds, or even with Leicester going into the final 4 I really like their chances. (This is where Everton sits relative to both those teams right now). All three of these teams are awful, but thankfully, 2 of them probably get to stay up. Also, I'm massively assuming that Nottingham Forest isn't going to get hot and pull itself out of the bottom 3.