This is no longer an emergency and I will change the status to resolved.
I did install the Quick Cache plugin and activated it with the default settings. The last few days have been better, as in no white screens saying, "Error establishing database connection".
But the webpagetest.org (on http://www.chowstalker.com) still gives me an "F" on "Cache static content", which is what I thought a cache is supposed to fix. Almost everything that "failed" is a static 250x250 image, so I will continue to figure that out and tweak as I go.
The other factor is a lot of inefficient or redundant queries related to getting my images into the Photosmash galleries. So that will be replaced with newer normal wordpress functionality. So for now... it seems to be working and I truly appreciate your advice.
You also helped me with some good links on the BH forum in this thread. My name there is Engineerly.
There is lots to learn as traffic and complexity increases and the fragility of shared hosting rears it's head.
ps: I'm going to repost most of this on bluehost to maybe help out someone there.