Intermittent Slowness

I have a site that is running intermittently slow, ranging from less than 2 seconds to 10 seconds page load speed.

I have installed W3TC and optimized settings so that getting a score of 91 in the Google Page Speed tool. I’ve tried turning off all plugins. I’ve cloned the site and moved it to another hosting account. I’ve hired someone to troubleshoot and tweak (they found a corrupt database file). All to no effect. The site intermittently still runs like a pig.

This is a client site that is on a dev url now, but I really need to get launched on their main domain, but I don’t dare do it with the existing performance.

Does anyone know of a reallllly good wordpress technical troubleshooter?

Thanks so much. Beth