Changing settings in php.ini require restart of apache service to be seen/used in Moodle.
The hint you've given (via hosts cpanel) could indicate your implementation is on a shared system. On shared systems customers share the resources of a single server. Hosting providers sell 'packages' which limit ... things like amount of HD space that can be used, etc. That also includes preventing customers on such server from using up more than their fair share of resources ... thus a cap on PHP settings - how long a script can run, how much memory can be allocated to run a script, etc. So if your server is on a shared system, you could contact the host helpdesk and inquire about your limits and/or a way to increase the time. IF on a shared system, the hosting provider may only offer a more expensive package ... or a VPS where you don't have to 'share' those types of resources.
The link your Moodle has to Server PHP info should disclose such information for you.
Timing out might only be one issue. Suggest turning on debugging and see what Moodle reports. There could be other issues related to php settings not in your control.
'spirit of sharing', Ken