Technically, selection lists can store attributes so you can select attributes as you would select anything else in MEL:
select -r nodeName.attrName
Anyway, the name of the channelBox control is mainChannelBox. The channelBox tool is dragAttrContext which is undocumented so you don't know the flags for the tool. You can write your own dragger tool that is independent of the channelBox using draggerContext.
It would be nice if you could control 3 attributes with one attr per mouse button but Maya API doesn't give you control of the right mouse button.