Eventually, I had to go into the database administrator on my server and paste in the SQL dump. However, this caused issues on its own (different admin backends, I suspect) and it was only after three hours or so of removing corrupted tables, hacking out unused data and generally cleaning things up that I finally managed to get things up and running.
And this morning a corrupted table brought the whole thing down again. Might I advise those running WordPress not to install a plugin called WP-User-Online; it was this that was causing a lot of the problems, with both my own server and with Longrider's original hosts.
Update: I wrote the original post two days ago – but it became lost during the recovery. Since then, someone called Jonathan has replied [from LR's hosting company]:I’ve spent some time reviewing the Slow MySQL Queries logs and what I’m seeing, up until the 26th when there appears a query should the addition of a Cache plugin, before this point resides thousands of slow queries, each suggesting use of Whos Online plugins, as well as other plugins that are poorly constructed, and have simply been running rampant on the server.
Yikes. Seriously, one should be very careful of all of these plugins: many, indeed most, are pretty robust, but it only needs one rogue to bring down your installation and, probably, your host's servers...