After having extricated the Disseminary domain from its infestation of bots (at least, for the time being), made back-ups galore, taken a deep breath, and squeezed my eyes closed — I updated my PHP installation and then, trembling, updated WordPress.
You see the result before your wondering eyes: don’t let the glare blind you.
Now, to resolve to keep it updated rather than waiting another mphsftml years…