I randomly stumbled upon this solution here: Why can't I install my service (runtime newer than loaded runtime)?
This solved my problem:
Here's what I had to do:
Right-click the service project in Visual Studio
go to "Properties"
Set "Startup object" to the name of the service (it had been set to> the value "(Not Set)").
Save.
Build Try to install again.It works! Yay! We can all go home!