Tommy is faster than Ricky, but even the greatest server can't work miracles on a slow wordpress site. In my experience wordpress is just really slow, buggy, and full of vulnerabilities. Pretty much anything else is faster.
If you insist on sticking with wordpress the next biggest culprit on speed is plugins. A lot of them are terribly designed, really slow, full of vulnerabilities, and a lot of the free ones are simply malware. Try disabling some plugins to see if that speeds up your site.
You can also check out a website like http://www.wpbeginner.com/wordpress-performance-speed/ with a checklist of things to try. It sounds like you may have already been down a few of these lists though.
If you want to move to Tommy we can move your site for you with minimal downtime for as little as $1.00 USD. If you think our service is worth more we recommend donating what you feel is appropriate. We've only had one person ever complain about Tommy being too slow, and honestly that guy was completely bonkers. He also said that Amazon Web Services was worthless for a production website because it was too slow, so take his criticism with a very large grain of salt.