The load I had on the front was none too rigid, I admit, and I also considered that to have a significant influence. On days where I had some stuff in the loosely-slung backpack, the tendency to wobble was a lot worse.
I still have the bedrolls assembled; I'll check them again with no load on the back and with extra strapping to make the load more rigid.
Perhaps there is something wrong with the frame on the whole - I have had the riding no-hands problem since the beginning. So I'll give it a good check-up. It's just that the bike felt really unstable while loaded.
Oh, and another thing - on coming back home, I found the front tyre quite soft - and I know that is a major factor too. I let some air out for the dirt roads, but don't recall that it was that soft.