I wouldn't use the r2+L2 hotbars on mounts and such. That could be your easy access third hotbar for battle.

Instead, put your companion abilities on some other bar (I chose 7) and make it so that r1 cycles only through hotbars 1 and 7 when your weapon is put away. Makes it tougher to command your companion during a battle (since you'd no longer cycle to the companion hotbar) but all you'd have to do is hold r1 and press the corresponding hotbar button to access the companion anyhow. (so it'd be r1+ dpad Down if you chose 7.)