OK, I'm all fixed. My own stupid mistake....but reading through your emails really helped me figure out what I had messed up, especially when I started looking at the caches.
The Chrome report indicated that something was wrong with first.js:
javascript.php:34 GET http://www.scholarsonline.org/~sodeveloper/ScholarsOnline/moodle/lib/ requirejs.php?file=%2F-1%2F/core/first.js
So I tried getting to the first.js file directly in the URL bar of chrome.
On MacOS (working), lib/src/ajax.js prints
On gentoo (not working), I get the error: JS file: /lib/amd/src/._mustache.js does not contain a javascript module in AMD format. "define()" not found.
There is NO lib/amd/src/._mustache.js file on the mac system.
Then I read through Ken's lengthy suggestion again and went looking at the moodledata cache directories paying attention to the dates of files.
I realized that in moving the moodle release from my Mac to the genoo system, I had tarred my already installed moodle directory, not the original directory as downloaded from Moodle...and there was cached data from the Mac in that file system.
So I downloaded a fresh copy of Moodle 3.1.1 from Moodle to my test genoo system, moved the "bad" moodle directory out of the way, copied in my config.php file, and voila! all works.
Thank you all for your help; I would not have figured this out without your suggestions about where to poke.