Thanks. So I abandoned the other route and followed your instructions. I got a general 500 Internal Server Error page when I tried step #8.
There are a few things that I can think of offhand which may have resulted in a problem. First, I was unable to do step #2 since I cannot access the forum's ACP. I tried searching for a way to do it via phpMyAdmin, but to no avail. I do have an active style that's not Prosilver, so I opted to search for anything related to styles in the database. I found and edited the phpbb_styles table, setting the Active status of all styles except Prosilver to 0 (three additional styles were installed, and they were all set to 1 before). But this made no difference on the live site; the alternate style I had active was still active. So I left it and proceeded, keeping my fingers crossed.
I was also unable to perform step #4. Again, because I cannot access the ACP. I recall that reCaptcha was definitely a functional part of the forum (i.e. registering a new user required it), but I don't recall installing a plugin to add it. I do not think I added any plugins, in fact.
Finally, I opted to skip files that already existed on the server while uploading the fresh phpBB files, such as images/index.html. Was this the correct move? They seemed identical when I brought some of them up in Notepad++.
I did download both my database and all files as they were to my local computer as a precaution.