and, when there's NO bass or 'pedal'
That would defeat the purpose of this exercise... I am trying to get you to learn how to gain chord options in jazz voicing. If you are on organ, you have pedals, and if you are playing piano in a trio or quartet, you will be using a bass player. If you are playing solo piano, then that is another topic entirely.
This topic is to strengthen your left hand comping chops and freeing yourself from the need to pound out the bass with your left all the time. It is a chance to stretch away from your comfort zone