So it's 'vanilla' for your hosting provider ... not 'vanilla' for all hosting providers. Ubuntu has been known to have worked with hosting providers and provide a special config/setup for the hosting provider (it's been rumored that Ubuntu on Amazon is such).
Confess don't run anything under Plesk, but sounds like 'big brother' to me. Mentioned .... couldn't put moodledata one level up from 'httpdocs' ... doesn't sound 'vanilla' Ubuntu to me either. Do you have any controls over Plesk and it's config?
As far as location of moodledata ... where is the location of cgi-bin diretory? or icons directory? With apache, those are normally present although not configured to be used on more 'vanilla' apache configs the directory in which they reside is accessible by 'apache' user/group on other systems. Document root typically has a 'home' directory (not by that name but on your system that appears to be 'httpdocs') but where is apache user's 'home'?
Am not criticizing hosting provider but wonder if they have their own FAQ's/customer docs for apps like Moodle that have some a-typical requirements?
Yes, setting up search with solr is proving to be interesting on various platforms. But like you said, it's worth the effort (with conditions). Maybe one of my 'nobbie' questions/comments concerning setup will trigger viewing the issue with different approach and lead to your solution.
'spirit of sharing', Ken