Well, I've been experimenting with using different papers and it definitely makes a big difference!
Someone (who shall remain nameless) was so kind and sent me samples of a couple of kinds of cs to try in addition to what I already had.
GP cs from Walmart -- bled way too much. Great for prisma pencils, not spectrum noir!
Copic XPress -- super smooth, great blending, no bleeding.
Bella's Bestest -- not as heavy, but blended well, no bleeding.
white paper from Joanne's sold in pack -- smooth but very thin, some bleeding.
Hollo's smooth heavy cs -- similar to Bella's, almost as good as Copic XPress.
(Hollo's is a store in Ohio that sells a variety of colors, weights, and textures of paper and cs by the pound. Pick what you want and they weigh it at checkout. Fun!
I will probably go with the Hollo's cs since it is available locally and is less expensive.