No you aren't overthinking, pick 7 is the hangman's slot. Any time I draw that slot in a league like this I do my best to try and trade down from that pick. In essence, I want a goalie but not at #7 so I try and go to a pick that warrants taking a goalie (9 onwards) and hopefully improve my draft position positively enough to warrant the move down. A normal strategy here for me is to seek swapping picks completely in rounds 1, 2 and 4.
You get an elite goalie at your first pick and improve your picks in round 2 and 4 by the difference between you and your trading partner's picks which is as little as 2 spots and as much as 5 - but can certainly yield a better player than you would normally get.
Failing that, I usually am looking goalies after picks 5 or 6 unless a super stud slides for some reason. I figure if guys picking 8 through 14 aren't taking at least one goalie in the two picks they have before I pick again then something is screwy. Goalie #8 is usually not a tier 1 guy with certainty - guys aren't going to opt for Thomas, Kipper or Brodeur because of their age so that thins out the tier 1 guys reasonably available. So I lean towards taking a goalie at 7 and should another youngish tier 1 guy slide to me at round 2 then oh well - I would rather be safe than sorry.