Version: JDK 1.7.0_60
Don't worry about the 2.0.2, then, that was me trying to find a newer version that worked. I'll just stick with 1.8.8.
So part of it seemed to fix itself after my ISP stopped being annoying.
The other part I had to fix with the method you posted. Perhaps this is a new thing for Windows 10? I'm not sure. Here's what all I had to do:
keytool -import -alias repo1.maven.org -file "C:\Program Files\Java\jdk1.7.0_60\jre\lib\security\maven1.cer" -keystore cacerts -storepass somepass
keytool -import -alias libraries.minecraft.net -file "C:\Program Files\Java\jdk1.7.0_60\jre\lib\security\minelib1.cer" -keystore cacerts -storepass somepass
keytool -import -alias georoot -file "C:\Program Files\Java\jdk1.7.0_60\jre\lib\security\geo1.cer" -keystore cacerts -storepass somepass
keytool -import -alias geointer -file "C:\Program Files\Java\jdk1.7.0_60\jre\lib\security\geo2.cer" -keystore cacerts -storepass somepass
(You can save there directly, just add yourself to the full control list for the folder.)
The certs referenced above can be procured from:
https://repo1.maven.org/ (First one)
https://libraries.minecraft.net/ (Last three; use the process here: http://docs.bvstools.com/home/ssl-documentation/exporting-certificate-authorities-cas-from-a-website )
I hope this helps someone in the future.