But will there actually come a time when I can just comfortably zip up a hill?

No; if you are comfortable on a hill, you are riding too slow.

A lot of it is mental--relative perspective.

There are people who I ride with to Nyack 6 months out of the year and they know the exact route we are going to take because we've gone there tons of times but they freak out and whine about the "climbs" every time.

Then you realize that a "climb" in NY might be a bump in the rode for people living in CA or CO.

Best thing to do is to straight-up attack the greatest climb you can find; then you know how bad it can get and how to pace yourself for anything less than.