Also, get some Steely Dan happening. Kid Charlemagne for example has a RIPPING bass line!!
Not familiar with that track but I was working on "green earrings" the other week... talk about 16th notes.
Play a lot of everything. Don't specialize in specific things. Versatility is where improvement happens and will end up making you better at playing the things you have the most interest in playing.
I couldn't agree more, yeah sleep now in the fire is challenging and its about as hard as most mainstream bass lines get, but just cause you can play one RATM song doesn't mean you have his style down, or comprehended. PLAY A LOT FROM DIFFERENT GENRES!
The reason rock bassists like Timmy C are good is because they studied bass outside of rock. I remember reading that Timmy was Jazz trained, and his lines are certainly funky. Also look at the other big rock bassists like flea for instance, his style is very funky (if you are looking for something challenging pickup the bass book to "blood sugar sex magic" and kiss the next 2 months of your life goodbye).
The only way to truly understand a genre is to understand a few other genres.
+1 to the meters, most old school funk is great for your level.
You want a bass standard that will push you try "Sir Duke" by Stevie Wonder....the solo will keep you busy for awhile, and the rest of the song will expose you to the fundamentals of a groovy bass line, and how to build a bass line to be more complex.
PS. Don't worry about your speed, it comes in time, be more worried about understanding what you are playing. I spent a long time learning to play hard stuff...countless nights trying to play some solo, or something like portrait of tracy...and it was all pretty useless, time much better spent learning 10 simple songs that expose me to new rhythms, chord progressions and music to listen to.