It may be shortened if you run out of movement.

You can either:

• move 10 feet and then long jump [Strength score] feet
• long jump [Strength score/2] feet
• move 10 feet and then high jump [3+Str mod] feet
• high jump [(3+Str mod)/2] feet

And each jump foot is deducted from your leftover movement. Therefore, if you have a high enough speed, then grappling doesn't really bother you.

For example, with 20 Strength and a speed of 60 feet, grappling a creature makes you have a speed of only 30 feet. You can move 10 feet and long jump 20 feet, or high jump 8 feet, which is the same distance you could jump without grappling a target. If, on the other hand, you had a speed of 30 feet, grappling halves this speed to 15 feet. Now, you can move 10 feet and then long/high jump only 5 feet, less than the original amount.

TL;DR: It depends on how much Strength you have, and how much speed you have.

It should work, but it's not as good as you think it is.

Your max carrying capacity is [15 * Strength score]. Absolute max. That means that with your 29 Strength, you're able to carry 435 lbs. That's your gear, plus their gear, plus them. That starts to add up pretty fast. Worse, if you're using Encumbrance rules, the move speed reductions start to rack up at [5 * Strength score].

Really, though? You're a 20th-level character, who's apparently dripping in high-rarity items.

Boots of speed only work for 10 minutes per day. You're not capable of casting enhance ability yourself (unless you get someone to cast it on you, and maintain concentration for you). This requires that you get up close, succeed at a grapple, and spend your time and effort on a single target, who has to be small enough and light enough to lift and carry. For that, you're reaping 6d10 damage per turn (an average of 33)... and that's assuming he didn't burn any movement on the approach.

By contrast, if your character, who's not particularly optimized for punching, decides to just punch the other guy (without using Rage or other buffs or most of his class features), he's taking three swings that do 1d6 + 9 (i.e. your Str mod) on each hit, for an average of 37.5 damage. Sure, it gets better for the jumpmaster on the next turn if he's still skyfalling the same person, but that assumes a fair number of things about the shape of the next turn, and a reasonably well-optimized beatstick can be doing a lot better than that with the sort of resources you're describing here. Bog-standard warlocks are throwing around EB for an average of 42 damage per turn (4 blasts of 1d10 + 5) at zero effort, and they're not even particularly high on the list.

It also assumes that your target is not in some fashion resistant to standard bludgeoning damage - something that is less and less reliable as you climb towards level 20.

So, basically, it's silly, it's a bit limited, it works, and it's not particularly game-breaking. It does have the advantage that you're shutting down your grapple target pretty hard, so if what you're looking for is "I'd like to be able to deal out some damage while I'm grappling, please," then it's worth something for that. Go ahead. Pull it out, show it off, have fun with it... but it's not actually all that impressive.