Some random pro-tips for using the MC-707, updated as I find out about them.
Holding down a step on a sequence and pressing FUNC when the single-step menu opens will take you to additional pages where you can nudge or pitch-adjust the entire sequence, and apply post-rec quantization.
Each pad in a drum track is its own "instrument", with a subset of synthesis features that are unique to the pad. You can access it by going into the Sound Edit menu for the drum track, selecting the pad you want to edit, and hitting Enter. This editing interface allows you to layer samples and offset them rhythmically, and gives you access to a filter, as well as a few modulation options, and some ability to control how that pad interacts with the MFX for the track.
In Mute Mode, you can hold the SEL button for a drum track, and press pads to mute them individually.
The track configuration when you start a new project does not seem to use the Drum+Comp engine by default, so don't forget to switch to that at the beginning if that's important for your project.