Thank you all for your ideas. Following a couple of suggestions to change the seat angle and possibly lower the bars, I've changed the position a bit and have a picture below.
The point about the seat itself is interesting. I've always felt with it that I was falling forward a little - tilting it back was an attempt to counteract that. I don't feel securely "perched" on it. Maybe the seat just isn't suitable.
It's beginning to sound as though I should try getting a bike shop to look at what I'm doing, and possibly also test some other bikes, to get some perspective.
Globalti: I take your points - I'm still trying to decide what I want from cycling, and what I can actually do. This particular bike is actually designed for drop bars, and came with them originally when I bought it (used). I ended up having to have those swapped for something more upright due to (other) physical problems which have since improved, hence my attempt to try drops again. The unusual stem, for example, is a legacy of that. The seat, though, was on the bike when I bought it, and (I assume) was used by the previous owner with drops.
I don't want to become a racer, but liked the idea of drop bars for (eventually) riding reasonable distances at a steady, quick-ish pace.
Finally: a couple of people have suggested that something (like a belt buckle) might be poking into me when riding. I don't think this is the case - I'm not aware of this while cycling, but will try to notice when I next ride.