The initial time to first byte for me just now was over 20 seconds. According to useful data the site is currently in the bottom 5% of average response time of websites which means from an end-user perspective it is (relatively) "crap". The lag appears to be more to do with the server rather than the code - although WP being what it is the code is a hurdle you're forever stuck with.
Doing things in the order below while checking results at each step will maintain a process of establishment rather than a process of elimination:
An Apache instance test would be handy (but we can't do that) so the first thing to do is log in to shell and check the server load by typing "uptime" at the commandline. If you see numbers greater than 100 then report the load to Support.
The next step is to delete any caches in WP and disable all your plug-ins (including cache plug-ins). You can re-enable things later - but for now disable everything and perform another response check to see if there is a radical change.
If there is still no change, check the domain settings via Panel, selecting PHP 5.4 FastCGI and dismissing all options except Extra Web Security. You'll need to wait a while for any new settings to kick in before re-testing to see if there is any difference, so do something else that doesn't involve loading your site for a good half hour.
If you have not seen a vast improvement by now, reinstate your plug-ins, ask Support to move your site to another Apache instance, and sit tight.
If you've noticed the site is more responsive it's time to reinstate plug-ins one by one, doing response checks at each step in another browser window or TAB.
Next, investigate the most appropriate caching mechanism to further boost response for your particular website. WP Super-Cache and W3TC are the popular choices.
PageSpeed and CloudFlare can be problematic, but give them a try - first individually, then together, starting with PageSpeed. If one or both play well with your particular website with all plug-ins enabled then use it/them.