I've seen threads on this, but never a clear and consistent answer about how to solve.

I'm on High Sierra, trying to install ANY v8.xx of MC (but preferably v8.0.0), and none of them allow me to, saying I cannot install on my hard drive because I need to install Java 1.6.

Well, I DID INSTALL JAVA 1.6. I checked it via Terminal and it confirmed it:

java -version

java version "1.6.0_65"

Java(TM) SE Runtime Environment (build 1.6.0_65-b14-468)

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Menlo; color: #000000; background-color: #ffffff} span.s1 {font-variant-ligatures: no-common-ligatures}

Java HotSpot(TM) 64-Bit Server VM (build 20.65-b04-468, mixed mode

What else do I need to do so I can install a version of MC that's newer than 7.6???

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Menlo; color: #000000; background-color: #ffffff} span.s1 {font-variant-ligatures: no-common-ligatures}

Java 1.6 (jre 6.0) is really old. Try installing the latest version and then install MC.