Thank you for looking into it and the prompt support. I disabled the chatbox temporarily and will take a look at that, so thank you for pointing that out.
As for outgrowing the host, I switched to their VPS - Cloud hosting, so I'm squared away in terms of resources. It's a pricey jump, but necessary for now as I look for another host next year.
As for the tasks not running, I worked through it with the host and it seems to be squared away, now. A few notes in-case it comes up in the future:
1. I use SiteGround as my host, and their shared plans do not allow alterations to variables such as execution time, so the Cron script won't work with their shared plans.
2. Even once on their cloud hosting, I was receiving errors with the cron task method. The reason being is the PHP Binary didn't work, and needs to be PHP-CLI with Siteground.
So instead of:
usr/local/php74/bin/php
The cron task had to start with:
usr/local/php74/bin/php-cli
Hopefully this can help someone else in the future, as well. You can mark this as resolved as we're squared away. Thanks again for taking the time to take a look.