Godaddy Email Solutions

So I have had godaddy hosting for several years with little problem, UNTIL I installed WordPress. Everything I read is “Stay clear of goaddy with WordPress” “Windows shared hosting is not great for WP” anyway I digress. Here is the issue. Because I use a shared hosting account, the multitude of plugins that use php mail() have serious issues. Right now, the only one I have been able to get to work is Contact Form 7 using WP Email SMTP with this handy little tutorial. However, any other plugin that has a mail function seems to fail. Especially, plugins like Thank Me Later and WP Mail. The worst part is that even if I got all functionality up and running with Godaddy and/or Gmail, neither allows “anonymous” sending, which is essential to WP Mail (as I understand it).

So the first question is, is there a simple solution or plugin that will run all php mail() functions as SMTP, since Godaddy hosting won’t run php mail (). (pardon my ignorance in possibly describing the actual function incorrectly). And the second question is what email servers will allow me to send “anonymous” email. I am not trying to be devious. I really just want to run a “tell a friend” contest and I have no way of knowing who is referring without a program like WP Email.