Can a Way of Astral Self Monk use wisdom related scores for jumping?

I have several questions on the interactions between the Arms of Astral Self and the Jumping mechanics. According to the 3rd level feature, Arms of the Astral Self:

While the spectral arms are present, you gain the following benefits:

  • You can use your Wisdom modifier in place of your Strength modifier when making Strength checks and Strength saving throws.
  • You can use the spectral arms to make unarmed strikes.
  • When you make an unarmed strike with the arms on your turn, your reach for it is 5 feet greater than normal.
  • The unarmed strikes you make with the arms can use your Wisdom modifier in place of your Strength or Dexterity modifier for the attack and damage rolls, and their damage type is force.

The Jumping session of the PHB states:

Long Jump

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.

This rule assumes that the height of your jump doesn’t matter, such as a jump across a stream or chasm. At your DM’s option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump’s distance), such as a hedge or low wall. Otherwise, you hit it.

High Jump

When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier (minimum of 0 feet) if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.

You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1½ times your height.

My questions would be, assuming that I have Arms of the Astral Self activated:

  1. Can I use my Wisdom Score instead of my strenght score to determine my long jump distance?
  2. Can I make a Wisdom (Athletics) check instead of a Strenght (Athletics) check?
  3. Can I use my Wisdom modifier instead of my Strenght modifier to determine my high jump’s height?
  4. Can the extra 5 feet range of the Arms of Astral Self be used when accounting for "extending your arms half your height above yourself" on the high jump, making it 1½ your height + 5 feet instead of only 1½ your height?

I am aware that some of the answers to these questions are up to DM discretion, so I would like to know, if possible, what would be the RAW interpretation and also how would you rule it in your games.

In advance, I’m extremely grateful to whoever takes time to answer these 🙂