Okay, so, one can make this better. The control panel is in fact called the "Super Control Panel", which is important to know, because the setting I couldn't find is called Live SCP in the menus. And you get to it with a single press of the OK button, once the camera is configured properly.

The relevant option is in the Custom Menu, under page D ( which is helpfully labeled "Disp / / PC" ), in a sub-sub menu named " Control Settings". Don't be tricked by the "Info Settings" sub-menu below that — that's only for playback.

This is on page 87 of the manual, and if you look on that page, it just shows a confusing chart of which possible control screens are available in which camera modes — P/A/S/M, iAuto, ART, and SCN all have a few different possibilities and can be saved separately. Options include Live SCP (what we want) and Live Control (a point-and-shoot border-menu like quick-access method which basically does the same thing in a different way)

The manual then points back to page 39, which shows how the info button cycles through possible screens. But — and this is key — despite the pictures and the text, it's not the info button that brings up the Super Control Panel. It is the OK button — but, if you have both the SCP and Live Control enabled, Live Control comes up first, and you then have to push Info to switch to the Super Control Panel. (This is the default configuration.)

The manual also points to page 22, where you would have learned what "super control panel" means, were you reading the manual straight through, and also page 24, where you can learn how "live control" differs. Sadly, this is one of those manuals written by someone who already knows what all the functions and menu items do, and it's really only useful once you've already figured it out. Looking at the manual when I was first confused only made things worse – I didn't get this figured out until I sat down and flipped back and forth and went through the camera menus and tried things and then referred back to the manual and then back again.

So, in summary:

In Control Settings under Custom Menu D, turn Live SCP on and Live Control off. Then, pressing the OK button while shooting will bring up the Super Control Panel with no fuss. One can then select an option and change it with a control dial without further button presses, or press okay to go to a sub-menu for that option.

Oh, and looks like it might mean "remote control", but it's actually for "beep sound".