I forget, does Swooping Dragon Strike take a standard action or a full-round action to use? And does it require you to jump up from adjacent to the target, or can you do a move action beforehand and then leap once you're close?
Also, what level was Swooping Dragon Strike? And wasn't there a Boost or Stance that improves your Jump checks? I forget, as I've only borrowed the book once, and only for a few days that time (I read a lot, but there's only so much I could memorize in half a week). Can't afford new books yet.
A monk/swordsage or monk/warblade could get a nice Jump bonus if allowed a move-action to approach first. Aside from that or playing a Thri-Kreen.....
At 10th-level of swordsage there could be 13 ranks in Jump, a +2 synergy bonus from Tumble, a +2 from the Acrobatic feat, a +3 from Skill Focus, a +4 from the Run feat with a running start, a +10 from an Improved Ring of Jumping, and a +7 let's say from 24 Strength (base 18, +2 from levels, and +4 Belt). So, right there is a Jump modifier of +37, or +41 when you have a running start of at least 20 feet before reaching the target. Also, I think a Swordsage's Discipline Focus, or the Blade Meditation feat, or one of the thingamajigs like that in Tome of Battle, would add a further +1 or +2 on your Jump check, but I forget exactly which it was.
Taking 1 level of Barbarian (so Swordsage 9/Barbarian 1, or whatever) for Fast Movement would add +10 feet to speed and thus +4 to running Jump checks. Sadly the Monk's FM is an enhancement bonus so it doesn't stack with the Improved Ring of Jumping.
You could get a +30 enhancement from a Jump spell cast by a friendly wizard of similar level to yourself, in place of the Improved Ring of Jumping's +10 enhancement, but the Ring doesn't require any allies. With Boots of Speed (or just a friendly wizard to cast Haste on you), you can get a +30 foot enhancement bonus to movement speed (which means +12 on running Jump checks).
Also, playing a Xeph (Expanded Psionics Handbook, a medium-sized race with 30 ft. speed but a racial ability to gain extra speed for 3 rounds, 3/day, which is +30 feet at 9th-level onward) could add another +12 to the Jump check if making a running start and using their Burst racial ability. Also, as a Xeph the PC would qualify for the Mental Leap psionic feat, which adds +10 to a Jump check when expending psionic focus.
If not playing a Xeph, it's just a matter of the Human PC spending his racial bonus feat on Wild Talent, and then spending a normal feat slot on Mental Leap (at 2nd-level or later, though, since it requires 5 ranks in Jump). And yes, there would be room for this feat in either case (sure, it'd be sub-optimal for other purposes, but it all of these +Jump feats would make Swooping Dragon Strike more awesome, wouldn't they?). Though there won't be room for the Blade Meditation feat or whatever if you do that (at least not until a later level), assuming you don't multiclass into Psychic Warrior.
The Speed of Thought feat would have to wait until 12th-level (unless multiclassing into Psion or Psychic Warrior for 1 or 2 levels) for lack of enough feat slots beforehand, but it also adds +10 feet to movement speed when psionically focused, so that would be another +4 to Jump with a running start.
And I'm just going to ignore the expendable psionic crystals that add a one-time bonus to a particular skill check (I forget what they're called, and don't remember what type of bonus they grant, so it might not even matter, if they wouldn't stack).
.......so, lessee what kind of insane Jump bonus we could get without just using a Thri-Kreen to begin with. I'll assume 10th-level, and no bonus from Discipline Focus or Blade Meditation (since I can't remember which it is that does the skill boost, or by how much). I'll also assume there's no friendly 10th-level mage available to cast Jump on the fella.
Kung Fu Zak, 10th-level Xeph practicioner of the Sublime Way, psychic warrior 2/barbarian 1/swordsage 9 (with terrible multiclassing XP penalties, but who cares
). Strength 22 (Xeph have a -2 Str penalty, unfortunately). Feats: Acrobatic, Speed of Thought, Mental Leap, Skill Focus (Jump), Run, Psionic Meditation (just to use Mental Leap more often in battle). Notable Items: Belt of Giant Strength +4, Improved Ring of Jumping (+10 Jump), Boots of Haste (+30 speed for +12 to running Jump checks). Using everything at his disposal when he jumps at the foe with Swooping Dragon Strike.
Jump bonus with no running start: +46 (so average check result of 56)
Jump bonus after 20-foot sprint: +82 (so average check result of 92)
On a die roll of 18 or higher with a running jump, he'll have a check result between 100 and 102.
