A Googler pointed me to a handy "how to" page HERE. Specifically it deals with the issue of Building Maker models that, once refined in SketchUp, sink into the terrain. You can see the step that explains how to fix that as well as how to do SketchUp edits at the link.
Above is an example model. Although the version I uploaded initially from SketchUp looked OK to me and I could export a KMZ file at the correct elevation on my computer, the KMZ generated online (at the "View in Google Earth" link on the model preview page) produced a sunken model.
A short edit later... and I think it's all good.