Hmm, I’ve gone from SC to W3 and am now happily on Quick Cache. Also, as a side effect (since WordPress cannot generate the page that is needed) I get 404 messages If I try to view Jetpack Stats. I have to reload the page several times for it to finally come up. Super frustrating..
If it makes you feel any better, I have the exact same issue on shared hosting. Switched off all plug-ins, reverted to default theme and yet still the CPU is spiking and maxing out. It is extremely frustrating and at the moment I do not know what to do..