Reference "Tai Otoshi," technique 1-4 of George Kirby, Black Belt Budoshin Jujitsu, Panther Productions, 1992.
Also, "Lopresti Spin," personal instruction from Paul Lopresti.
Step 6-9 of Empi are the "swallow cluster," including the downblock that most people think is part of the next cluster. (Step 10-13 and 26-29 are the identical clusters later in the kata.) We begin in left downblock position facing north. Step 6 is the furi zuki (rising punch). In step 7 we step in (kosa dachi), bring the right fist back to the left shoulder, and punch downward with the left hand. Step 8 is the "swallow" position: we turn south in front stance, lean the torso sharply to the south, look back over the shoulder and downblock with the right arm parallel to the extended rear leg. Step 9, we straighten up without stepping, face to the south, and downblock with the left arm.
We know that Empi (Wanshu) is called "the dumping kata" because it teaches throws. We expect to see beginner techniques in the beginner katas, so we should expect to see beginner throws in this one. It happens that the "sparrow" posture in step 8 bears a striking resemblance to the tai otoshi throw, which is a beginner technique in both jujutsu and in judo. Shotokan students first encounter this throw in Heian Shodan, step 9. Here's a graphic borrowed from http://www.judoinfo.com.
Budoshin's tai otoshi (technique 1-4) is particularly apt for this cluster of Empi because it puts an elbow under the opponent's chin. Your partner is in a fighting stance, left foot forward. Take his right wrist in your left hand (perhaps after blocking a punch). Grasp the cloth at his right shoulder using your right hand (after step 6). Step in and place your right forearm under his chin (step 7). Turn to the left to turn your back to him as you step in deeply with your right foot (step 8). Place the toes of your right foot on the ground in line with the toes of his right foot. (Only the ball of your foot will be on the ground, not the whole foot.) Now pull his arm around to your left as you use your elbow to push his head around in the same circular motion. He spills over your outstretched leg and falls heavily on his left side.
In the combat version of this throw, you would keep your forearm under his chin and drop with him, driving the back of his head into the ground. That technique satisfies the Waldow Principle. In jujutsu classes, this part of the throw is not performed. The elbow is removed from the chin early to allow the falling partner to land safely.
At this point the opponent is on his back on the ground, and you still have a grip on his right wrist. From this point you can apply the Lopresti spin, as described here. Pull his arm strongly to your right, spinning him end-for-end on the ground. This is the block in step 8. Then pull his arm back in the other direction, which rolls him over on his belly. This is the block in step 9. He ends up with the right wrist, elbow and shoulder all locked in a painful ude gatame pin.
What about the rising punch (step 6) and the groin punch (step 7)? These appear to be atemi strikes, designed to unbalance and disconcert the opponent. Jujutsu and aikido students use very minimal atemi to achieve unbalancing, often using just the tip of the thumb to jab between the ribs. Karate students, however, are free to shatter the opponent's teeth (step 6) or punch into the bowl of the pelvis (step 7) to destroy his balance and coordination. These attacks just make the following throw and submission even easier to perform.