I found a solution after more carefully reading: Mouse Clicks: Configure different functionality for long or short presses
The trick was to set my short press "mb click: keep default behavior" action with trigger on mouse up and maximum hold time of 0.2s (I tested diff values and 0.2s felt the most natural and non-conflicting with the long press config) so it doesn't activate when I want to trigger the long press. It's mentioned in step 4 of the linked tutorial:
Case closed, thank you!