The rules you've quoted on combining magical effects are unambiguous - these two effects stack, since they're not from the same source.
As for how they stack, the answer is your fourth choice. While in previous editions the rule was that multipliers stacked additively, not multiplicatively, 5e has no such rule. Likewise, 5e has no concept of "base value". When you use Step of the Wind, your jump distance is doubled. Then when you use Jump, your jump distance is tripled.
It should be noted that High Jump, like Long Jump, states that each foot you jump costs a foot of movement, so the distance you can jump is still constrained by your move speed. Obviously there are numerous methods of getting a very high move speed, but it is still an important constraint on your ability to leap skyscrapers in a single bound.
Also worth noting is that, as the highest rated answer on your linked question says, you still take falling damage when you jump, so another constraint on your ability to jump into the stratosphere is the damage you will take when you land.
And finally, to dismiss any concerns about balance, I have to point out that this requires a 1st-level spell and a 2nd level Monk feature to pull off, and Fly is a 3rd-level spell. And that's not even mentioning the fact that you can reasonably expect to be fighting flying enemies right from the start at level 1. This "super jump" is a cool trick, but ultimately not that useful or powerful.
Jump does not let you bypass the 'Speed' restraint on jumping. But the ring is still useful
As to Jump (and the boots) not increasing your speed, here is some Developer commentary on the matter, specifically addressing these effects.
Question posed: "Can you jump farther than your movement when using magic i.e spell Jump & boots of striding and springing?"
To be clear, things like the jump spell don't increase speed. You can jump crazy far, but your speed caps it. -Crawford
Are you saying you can't jump farther than your speed even with Jump spell or Boots of Striding and Springing? -Followup Question Asked
Every foot jumped costs movement, so you can jump farther than your current speed if you take the Dash action. -Crawford Again.
Source
So, no. Neither the Jump spell nor the Boots of Striding and Springing allow you to exceed your total Speed in distance jumped, though taking the Dash action allows you to move your full Speed a second time during the turn, effectively increasing your Speed by 2x for the round. This lets you actually get some use out of your massively boosted jumping distance. This would rather plainly imply that the Boots of Striding and Springing are generally superior to a Ring of Jumping.
Where this is not true is when you start combining magic items. For example, if you get your hands on a pair of Boots of Speed. Naturally, you can't wear two pairs of boots...but you can wear a pair of boots and a ring. This combination takes two bonus actions to fire up, but then you have a full minute of doubled running speed and tripled jumping distance, without having to take the Dash Action. And because you can get 10 minutes of boosted speed from the boots per day, you can do this 10 times a day. So you have all the mobility of someone Dashing around in Boots of Striding and Springing, but still have your Action free to use.
So, taken in isolation, it does appear that the Boots of Striding and Springing are generally superior to a Ring of Jumping. However, you have 10 fingers for ring-wearing, but can only wear one pair of boots. So the ring is better for combination work.
Best Answer
This should work.
When the jump spell says "jump distance", it is most obviously referring to the rules for long jumps in chapter 8 of the Player's Handbook:
This is how you determine your "jump distance", and this is what jump was originally referring to. Now, Rabbit Hop provides a completely different jumping mechanic, but it does provide a method of calculating a "jump distance":
So while this isn't the "jump distance" the jump spell was originally referring to, as Rabbit Hop was published some seven years after the jump spell, it is still a "jump distance" - it tells you how far you can jump.
It is important to note that while conventional jumping expends your available movement, using Rabbit Hop does not use your available movement, and can even be used if you have no remaining movement this turn (and your speed is not 0).