OK, here are a couple off the top of my head that don't need you to be a brayer expert!
Bouncing brayer - the tutorial
here uses a Kaleidoscope pad but I've done it successfully by inking up a brayer with two or three individual pads. If you use three, it's easiest to ink up the centre of the brayer first to get a "stripe" then ink either side of it with the other pads.
Ink your embossing folder with your brayer before embossing it (tutorial for Faux Letterpress
here is the sort of thing I'm thinking; Beate actually does it directly with the ink pad - I've had more success with even coverage if I use a brayer)
If you feel like getting to grips with the brayer a bit more, try some brayered skies (tutorial from the master - Michelle Zindorf -
here).
You could also do some sponged stuff - maybe stamp and clear emboss some images for a resist pattern as well as just sponging "cloudy" backgrounds with a couple of complementary colours.
Maybe do some "wrinkle free distress"? (tutorial
here) - although it's usually done with Distress ink your Classic ink should work OK.
I'll come back if anything else pops into my head!