Everett will probably become much better this year. He is the most sudden TE I've seen since Aaron Hernandez. He is a playmaker just waiting to happen.
But Higbee doesn't impress me. If the Rams don't feel he has improved at the OTA's I could easily see them taking a good blocking, decent receiving, TE as early as the 3rd, no later than the 4th round.
No reason a team can't find good to very good good, even future All-Pros, in the middle to late rounds. And Snead has done a pretty good job at that lately.