Got command line access? There is a script for installing in moodlecode/admin/ called install.php.
Since that takes apache out of the loop it might actually use less memory.
If you don't have access to command line, me thinks asking provider to do it for you might be risky ... not that they couldn't do it ... question is would they and if one has troubles installing what of running it over a long period of time .... past initial install ... Moodles only grow after initial ... they don't get smaller.
So ... you might have to opt for a package from provider that allocates more resources to your setup ... they call those VPS's - managed and un-managed. Managed means they take care of updates to OS stuff, but customer handles apps.
2 cent suggestion/advice offered for free!
'spirit of sharing', Ken