I made that last post while I was tilted. After a shower and some reflection I realized I was just focusing too much on fishing for combos - i.e. not actually relying on my fundamentals. It's any easy trap to fall into when learning a new character.
After my second session my GSP with Mario shot up a ton. I just had to go back to focusing on playing around my opponent rather then trying to force my own aggressive play style onto them.
I'm used to playing heavies, who can easily dispatch opponents at kill percents with very soft reads in neutral. Mario pretty much has to rely on getting a read in advantage state to get a kill until higher percents, as his options are either to edge guard or throw out a smash attack (which is very risky outside of advantage). I'm not used to having that kind of patience when it comes to kills, so that was a bit of a learning curve to me.
I didn't mean to imply that he had the same kill power issues as, say, Pikachu.