Well, I finally decided to upgrade my Debian to the current stable version. Everything actually went extremely smoothly, even if I wasn’t all that optimistic in the progress.
Well, almost everything. Of course, a few pieces of software made major version jumps, so I went through some settings and made sure those were in order. I also got rid of some private backports, since many of them are now available to me in the stable repository. The only crucial issue I faced was that my speakers didn’t play sound anymore. After some investigating I found that timidity was grabbing the sound card very selfishly and ended up removing it. PulseAudio immediately gained control of it again.
I have to say, while I’ve never had a dist-upgrade without hiccups, I’m tempted to say that this one really was a joy. Maybe the times of broken systems are finally over for me.