Just wanted to update the original post.
In the end, Bluehost told me that my account was exceeding the allowable 20% CPU useage for shared accounts, so they were throttling my account. I found that somewhat hard to believe. However I looked at what I had on my site anyway, but did not find anything that should have been using so much CPU. I asked them what should I remove, and their response was to tell me to do the same things they had already told me to do, which was installing cache plugins. I had already done that. They told me until I could lower the usage, the problem would remain. So I decided it was time to change hosting services.
Over the past weekend I completed the hosting change. Oddly, the new host also has a limit on server usage, which is 25%. Being concerned about that, I asked a lot of questions about limits and throttling before signing on with them. I saw in their demo control panel that they displayed a CPU real time usage amount, and asked them if that would be in my control panel. They said it would, so I went with them. After completing the transfer and my site was fully propagated to the new host, I monitored CPU usage. Not once did it go above 0.2%. Most times it was 0.1% or less. So what does this tell me?
Either Bluehost is using smaller capacity servers, or they weren't being truthful about what my throttling was set at. My guess is both. I wouldn't be surprised if they are severely overloading their servers in an attempt to save money, and in doing so, have throttled their customers to a very low rate. I Goggled up Bluehost, and what I found wasn’t pretty. They have a lot of unhappy current and past customers, especially over the past few months.
At any rate, the change over is done, the site is loading in less than one-third of the time it was before. Only time will tell if it remains that way, but I will say I did an awful lot of research prior to selecting a new host. And I wasn’t able to find one single negative thing on the net about the company I went with, and they have been in business since 2002. It took less than two hours for them to move my site, less than one hour to start propagating my DNS after I directed Bluehost to them, and I was in business.