Really, you have to go with what the company offers. There is just no other way and if you try to reach out to a support channel where they do not provide support, you're just going to get redirected to a channel where they do offer support (the help desk for example).
If you're not happy with your hosting provider (as they only provide support over the helpdesk), the only other option is to find a new provider that offers the support channel you prefer.
You can look if your provider offers: Skype, tickets/email, live chat, phone and even over social channels such as Twitter / Facebook.