I finally realized, or discovered, that installation of the Wolfram Free CDF Player does create an entry in the user's data files such that one can install non-Wolfram applications. In Windows it's in:

username/AppData/Roaming/WolframCDFPlayer/Applications

If you include an Applications/applicationName/FrontEnd/StyleSheets/style sheet, then the CDF files can use it.

However, the bad news is that, in my example at least, the package code doesn't work. It may be that DynamicModules aren't supported.

My example had a custom style sheet, DynamicModules with movable (and sometimes constrained) locators that carried lines with them, dynamic textual displays. It also had a separate CDF document window that could be launched with a button from the primary CDF document. The separate window had sliders and rotatable 3D graphics. The only thing that worked was picking up the style sheet and the movable locators.

However, again with the example I used, if I place the extra application into the Wolfram CDF Player program files, then everything works perfectly!

So it's another case where a miss is as good as a mile. Perhaps there is something simple I'm missing, or perhaps there is a reason.