Thanks, all - sounds like I should just stick at it.

The thing is that I work from home (ha!), so I have no "mandatory" commute. I'm trying to go downtown a couple of times each week, to run errands and to exercise the bike. It feels like I am steadily getting better - not faster yet, but much less tired than before. The guy from my LBS adviced me to work at increasing my cadence, and that has helped a lot. Uphill, I can now ride lower gears at a regular cadence (whereas before I'd feel that I was pedaling too fast and going too slow), and downhill, higher gears at a faster cadence than before (whereas I used to feel that the gears "topped out" and I needed more).

Now I'm actually noticing when bikers are going uphill, struggling with too high a gear and a really slow/painful cadence, and it seems that they could just switch to a lower gear...