I found previous versions of the google-play-services.jar (dated 6/12/15) and android-support-v4.jar (dated 5/7/13). The site documentation for the FusedLocationProvider library states that it is dependent on google-play-services, android-support-v4, and GPS libraries - and additionally, "If you're using Google Play Services version 27 then you need to use FusedLocationProvider version 1.30" - I'd been using version 1.10 (seemingly w/o any problem until I just recently updated my Android SDK - which then updated google-play-services to version 28). I don't know if my previous google-play-services.jar (dated 6/12/15) was version 27 or not.
In any event, I installed the FusedLocationProvider version 1.30 lib files and played around with different configurations of the google-play-services and android-support-v4 libs, and finally got my application to compile and load successfully to my USB-connected Nexus 7 using my previous versions of the google-play-services and android-support-v4 libs.
So, it would seem that the newer google-play-services and android-support-v4 libs are problematic with the use of the FusedLocationProvider lib.
I'd appreciate any other feedback on this subject...