[Subscripto Woocommerce] Problem with Wp-Cron, scheduled subscription payments

Long story short, I inherited a client last fall and the website has had some bugs that are slowly getting worked out.

Despite the long process of overhauling, the website has experienced some growth. Currently the website has about 30 products that currently work on a subscription system (using woocommerce + subscripto). Customers sign up and can get a weekly, biweekly or monthly product. Currently it has around 200 weekly renewals.

For the past few weeks, the subscriptions take forever to renew, generate payment etc. Stripe say’s everything is okay on their end, and the plugin developer says it’s an issue with WP-Cron being backed up / not enough visits to the website.

Our host believe it’s our shared hosting plan not having enough resources. I’ve never experienced anything else that would agree with that statement, the website is very reliable. They suggest moving to a VPS and paying almost 20/month more. Are they just trying to get more money?

I’ve seen some websites that talk about disabling wp-cron and setting up something in Cpanel. Could this possibly work and avoid us moving a server (for now?)

Something like this? http://churchthemes.com/2013/11/18/using-real-wordpress-cron-job-increased-reliability/