Good news. After a week of fruitless efforts, I finally got the 128gb card to work, thanks to the developer of Apps2SD. He replied back with a suggestion within a day of my emailing him. It ends up the card just needed to be partitioned with GParted using a live linux boot up CD. I didn't have one at the time, but I was able to easily download the ISO image from the web. He also said to use EXT4, but I used EXT2 instead because that's what I am using successfully for Link2SD in my other devices and so far it's working flawlessly in the Stylo. So really, the key in my case was to format it from within Linux using GParted.
There must be something quirky about how Windows handles the formatting of large capacity cards. As I said, I had no issues formatting a 32gb card from within Windows and having the 2nd partition properly recognized by Link2SD and Apps2SD. It was just the 128gb card that wouldn't behave.
So right now, I have the first partition at 106gb and the 2nd partition at a little over 11gb. I am using Link2SD currently because I find it a little more stable and faster than Apps2SD. However Apps2SD does everything Links2SD does, plus more, and it has a nicer interface. It's a relatively new app, so if the developer keeps improving it, I'm definitely going to revisit it in the future. Right now it's free, but the developer will be going to a paid model shortly. Don't know if he'll keep the free version the way it is (with all features enabled) so if anyone wants to try it out, now's a good time to download it.
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Link2SD not recognizing 2nd partition ... Anyone know why?