The First, Somewhat Rigorous Solution

Turning tcp window scaling off in the kernel gets us rid of the symptoms (thanks to Erik for figuring this out). Reboot or wait long enough for the network trouble to have subsided, then do:

jurjen@testhost:~$ cat /proc/sys/net/ipv4/tcp_window_scaling
1
jurjen@testhost:~$ sudo sh -c "echo 0 > /proc/sys/net/ipv4/tcp_window_scaling"
jurjen@testhost:~$ cat /proc/sys/net/ipv4/tcp_window_scaling
0

This makes random articles fetch in a couple of seconds, some in under a second, some in a dozen seconds or so.