While I don't use Netcup's web hosting offering – what prevents you from simply moving the app folder below the public folder?
Well, nothing. But I don't want to expose the app directory to the internet for no reason.
I guess we are talking about a netcup Webhosting offering here. You should change the open_basedir setting. This can be done in the WCP (Plesk) PHP settings. There are two alternative open_basedir settings available. The one which is the default and very likely active in your case is the one with {DOCUMENT_ROOT...} in it. This will allow PHP access to files withing the document root and below plus some system paths. You should choose the other one with {WEBHOSTING_ROOT...} instead, which allows PHP access to the entire webspace. So this one should work with your software.
Wow, thanks so much! I misinterpreted the meaning of {WEBHOSTING_ROOT} so I didn't think it would work. Many thanks!