Stick in center console, how to easily write down clearances and other similar information?
One technique many airline pilots use is to enter letters and numbers on the FMC keypad to use as a reminder for complicated taxi instructions. 

“taxi via Hotel, cross 15L, right turn Bravo, hold short Alpha One” could be entered on the keypad as: HX15LB/A1 or possibly H X15L B/A1

There really is no requirement to write down this type of instruction, or any VFR clearance. It is just a reminder and makes for good airmanship.

Many FOs in the right seat seem to use their left hand when entering data in the FMC as it can feel awkward to reach over and punch buttons with your right hand.

In your case you might be able to use an iPad or some other type of electronic device on a knee pad to punch in some “shorthand” with your left hand to help you remember what ATC says.