Hi Brian,
I have an E-50 which is very similar, but it's put away right now. If I remember there's a way to do what you want without using Makeup Tools. Press the "Mixer" button until the touch screen shows the volume for all style parts. Turn the volume to zero for everything but Drums & Bass. Then save these settings as a user program.

Note you can still use Cover & Makeup Tools to easily change the drum & bass to Acoustic, Pop, etc. And I'm pretty sure the volume of the other parts will remain zero for all style variations and fills, so you still have some flexibility with the style.

One last comment... Is your E-60 running the latest OS v1.1.1? My experience with Rolands is that they're pretty buggy out of the box. Using the most recent OS solves a lot of problems. Good luck!