Yeah I'm just as baffled as you are.
How can a WordPress overload the server. But from what I hear from 5xmom.com she has had that experience too running on her own VPS server. However, she has at least 20-30x more traffic than I do.
Under the shared hosting account I have no access to any tools that can pinpoint what caused the CPU overload
Right now, my own website is unavailable daily at certain times of the day. 5-15 minutes outages. I dare not even complain to Exabyte support (like I usially do) now because I feel the finger pointing will come back to me again and I get suspended once more.
I wish I can migrate to slightly better shared hosting like their e-biz account. I have another website with that account and the congestion or outages never happen there (or at least I've never seen it). But I've already paid for the year.