Ditto the EH hosting rec. The servers are geared for running dynamic, db driven sites.
Intermittent slowdowns may well be server related- particularly in a shared environment. But it could be something like pulling in off site content (if you do that) or a cache that doesn’t clear properly. Something along those lines. So if you want to poke your current site on your current host, we can always do that as well.
That said- I love it when troubleshooting something on EH, because I know the server setup is solid.
Also- going to shift this to ‘General’ forums where it’s a bit better fit.