Understanding the mechanics of a satyr’s mirthful leap

I apologize if this question has been asked in this form or another, but I am still having an issue calculating how to utilize a satyr’s mirthful leap, and how it would affect the character moving forward, focusing on the math and stats. For this question, I’ll use the DndBeyond stat block’s 12 Strength as a fair basis and perfect rolls for maximum distance.

The satyr’s mirthful leap is stated as follows:

Whenever you make a long or high jump, you can roll a d8 and add the number rolled to the number of feet you cover, even when making a standing jump. This extra distance costs movement as normal.

while the calculation for long jump states:

When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.

So adding everything together as I understand it, a satyr can either clear a 20ft chasm with a 10 ft leap (12ft for strength and 8 for their ability), leaving them 5 ft extra in case something goes wrong, OR can clear a 13ft chasm ([12/2]+8) without a running start. This means the satyr has the ability to use nearly all his movement in one long jump, correct?

If that is the case, then:

  1. If your satyr had to cross a terrain during 1 round by leaping from platform to platform (say to cross a river, or avoid the many pit traps in a sealed hallway), how would the mirthful leap be applied? Without a running start, would each leap be up to 13ft? Would that only apply to the first jump? Or would the mirthful leap of the prior jump be considered a running start for the next, allowing them to jump to the next platform up to 20ft away?
  2. Would this not make modifiers like Boots of Striding (tripling jumping distance up to character speed) useless?