Just thought of another approach you might take with your hosting provider .... everyone likes to keep up with the Joneses - true of hosting providers as well.
Do some research on other apps they host ... like Word Press or Joomla or ? with their shared hosting customers. While Word Press and/or Joomla's do not have Barricuda requirements the folks who are professional DB admins and do DB's for a living seem to be agreeing that Barricuda is better. Google for Percona ... they are one such company.
Shared hosting providers should be interested in providing the best for the buck ... even if cheap. And they also should be concerned about use of resources ... their resources ... like shared DB servers for those shared hosting accounts. As well as *your* data.
That's probably an uphill battle if you desire to stay where you are with what you have, but ....
Will say this ... moodle security is pretty good ... and Usman is correct, there are (shudder) folks still running 1.9.highest. But consider ... no updates for anything including security issues. It could be a matter of time ... that's all ... before a bot (or human) targets your site. In comparison, it's kinda like trying to keep Windows 98 or Windows XP alive - certainly one wouldn't do that!
If you are willing to gamble ... go for it ... but don't be surprised if you loose and that might occur at the worst posssible time. Not trying for FUD ... Fear, Uncertainty, Doubt ... just 2 cent opinion ...
'spirit of sharing', Ken