One should check the input side rectifier too. Chances are that it is only that poor little NTC that worked as a fuse.
You were right.
The bridge rectifier was bad. Actually I could see it in circuit with the DMM.
I replaced the original (GBU 408) with a KBL406G salvaged from a dead PC PSU. I got a almost identical NTC (a 10D-9) from a broken laptop transformer.
The cap measured 136uF (~-10%) (I don't have an ESR meter to check the cap ESR), so I left it in place.
Replaced the fuse and the Rigol is now alive.
There is some noise/distortion that changes when I change the DC offset.
I haven't changed the 150uF cap. I'll probably order the correct components to see if it fixes the distortion, but giving that the scope is alive I'm happy.