Here was the problem (simplified):
Main directory one/two/MainProgram
which depended on one/util1, one/util2, one/util3
Some of the complaints were of the sort, if one/util1/Foo1.java uses class defined in one/util2/Foo2.java, it couldn't see it. "symbol undefined".
Often Foo1 would use something in Foo2 and Foo2 would use Foo1. I don't know if that contributes to the problem.
Furthermore, a file like one/two/MainProgram/Bar.java would try to import one.util1.* and be told the package didn't exist, and that the symbol Foo2 or one.util.Foo2 didn't exist.
I put util1, util2, util3 into one project called "Util", and one/two/MainProgram into a different project, called "Maine" and used the "Add Project" button under the Libraries window to add the Util project as a library for Maine.
I still get complaints about not being able to find the symbols defined in the same directory while I'm in the editor, but when I do a "build project", I don't get complaints about symbols undefined, and it does say "BUILD SUCCESSFUL" at the end.
Not a complete solution, but an improvement?