"...guessing the settings in PHP.INI. I don't know it for a fact because I try to stay outta PHP.INI and generally avoid messing around with it's contents..."
Well unless you make errors you will never learn much, I would suggest that we learn more from our mistakes than we do from what we get right. When you trash something, you learn how to avoid it do you not?
Yes, there is a setting in the PHP ini file... in the section Resource Limits - look for max_execution_time see if that is set to 30, if it is, then change it to 240. You may also want to change the script memory limit to 256. There might be something else, but I have not found it an issue. These settings work with a 500MB file, and that is the largest file I will allow on any Moodle I admin. This is done for the simple, practical reason that I have set the file upload limits to 512MB. Anything biggest than that and you hmay have a serious issue anyway.