I should note that there's an extension that lets you modify some of the
settings from the web interface - Site Settings:
https://www.mediawiki.org/wiki/Extension:Site_Settings
It doesn't modify LocalSettings.php; it overrides it. It only covers a
fairly small number of settings, but maybe they're all that you need. Also,
it has hooks so that you can add more.
There's also the Configure extension, which lets you do the same thing but
with more settings (and a less-nice interface, in my opinion), though it
apparently doesn't work with recent versions of MediaWiki:
https://www.mediawiki.org/wiki/Extension:Configure
-Yaron