Reference, Kendo, Taro Ariga's Kendo Principles DVD set.
Also, "Ushiro Nage" (technique 3-6 and 4-4), "Ashe Yoko Nage" (technique 4-7), "Hanbo Ashe Ushiro Nage" (technique H-3, disk 7), George Kirby, Black Belt Budoshin Jujitsu, Volume 1, Panther Productions, 1992.
Also, "Gracie Kick Defenses," Gracie Jiu-jitsu Self Defense 4 DVD Set by Carlson Gracie, Jr.
Steps 16-18 of H. Nidan are the gyaku uchi ude uke (reverse inside block), the mae geri keage (front snap kick), and the gyaku zuki (reverse punch). Steps 19-21 are the same techniques on the opposite side.
Unarmed Interpretation
Step 16 is a very odd block. From step 15 (knife-hand block facing southwest), the trivial defense against an incoming punch or kick would be to shift stance to the south (as the kata does) and perform a left inside block or a left downblock, depending on the attack. The left arm moves only inches to perform these techniques, but the kata doesn't go down this path.
Instead, we block with the wrong arm; we perform a time-consuming sweeping stackup; and we end with the hips twisted into a painful gyaku hamni position. I was taught to reverse-rotate the hips to make the front of the torso face the east-- meaning that a punch or kick hitting the front of the body would be spun off to my left.
So what is this weird position?
Sukui uke is the general term for the family of "scooping blocks" that let you catch a person's foot when he tries to kick you. There are several sukui uke blocks. Step 16 of H. Nidan used the right arm to swing right-to-left in a "reverse downblock" that wraps around the leg and catches it in the "V" of the "inside block." The twisted hip position lets us be closer to the enemy at the critical moment. If we mistime the block slightly, the kick just glances off the body wall and does no real damage.
Having caught the leg in the bend of your right arm, use your Shotokan hip power to snap your inside block back to the right, bending his knee and forcing him to turn to his left (to your right). He'll be helpless, hopping on one foot, with his torso leaning away from you. His groin is wide open, and perfectly positioned for your incoming mae geri keage (step 17). He can't block it; he can't dodge it. This is another "twist and shout" application.
After kicking his testicles, the following reverse punch (step 18) seems almost superfluous except as the setup for the next sukui uke technique.
Note that this application satisfies the Waldow Principle. He's not going to get up again and fight anytime soon.
Nito Ryu Interpretation
Let's continue the sword-fighting interpretation. When do kendoists make a circular, sweeping gesture similar to the sweeping block in step 16 of this kata?
Some kendo schools (not all) practice a family of techniques called Maki Waza, in which the opponent's blade is scooped out of position (or out of his hands entirely) by "wrapping" your sword around his in a circular motion. This video clip of Maki Age will give you the idea. Other schools have stopped teaching sword disarming, apparently because the rules of kendo don't reward you for stealing your opponent's sword. I think the Shuri bodyguards would have cultivated this technique.
To try a simple version of Maki Age, have senpai hold a bokken in the classic two-handed grip: right hand up against the tsuba (guard), and left hand lightly holding the kashira (pommel), usually with a significant gap between the two hands. Use your bokken to engage his. Push the blade of his sword back toward his left shoulder, and then rotate it rapidly in a clockwise circle. If he hasn't seen the technique before, odds are that he'll lose control of the weapon entirely and it will fall to the floor. In fact, it may fly away as you saw in the video clip. (Be careful of hitting mirrors, windows, or bystanders. The bokken flies a long way.)
That's step 16, the "scooping inside block" motion of the kata. Make Age twirls his sword out of his hands and drops it on the floor.
When the sword hits the floor his natural reaction will be to pick it up. He'll bend over to reach for it, and you can kick him in the face (step 17). The gyaku zuki (step 18) runs him through with your second sword.
Steps 19-21 are the same techniques executed on the opposite side. The maki age "wrap" works in both the clockwise and counterclockwise directions, and against both a one-handed and two-handed grip.
Maki Age is only one of several similar techniques taught in Maki Waza and its neighbor, Uchi Waza. In Uchi Waza you learn to beat the opponent's sword away to create an opening. In H. Nidan, Matsumura offers only the first lesson in the series, as is appropriate to beginners.