After going back an forth with the hosting provider over this issue it turns out the limit is set at the hosting level and there's nothing I can change in .htaccess nor php.ini that will do anything with the file upload limit setting. So, although I was getting the correct / modified value, the server would not take those into consideration, hence the problem.
Lesson learned: if, no matter what you do, the change is not reflected in your moodle setting, then there might be an overriding policy that is preventing the change to take effect.
Thanks all for your help!