I asked our MediaWiki administrator, and he has questions* - any help in answering them would be greatly appreciated:
...it seems that we need to allow the api in the localsettings and take care of the rewrite rules... can you do a little research into the downsides of that? Do you know if a) accessing the api is necessary? b) if there are any problems associated with opening the api for mediawiki?
* He would normally do more research himself, but is currently working in a remote location with little internet access... and I don't have the technical understanding to research it properly - thanks for your patience!