Ron...thanks for thinking of me.
Jean...I might be able to add something here because, coincidently, for the last two weeks we've been focusing on doing kihon dosa with partner in class so I have been thinking/discussing/remembering/playing with it in detail.
I think the short answer to your question is that you have to find the point of uke's resistance and then go around it. If you want to see why I say that read on for my long answer to your question
Hiriki no yosei ichi
I think the first thing to think of is why we practice this basic movement and what its purpose is.
Basically, my answer to that question is that hiriki no yosei ichi is a method of moving your body from one place to another by moving forward in a straight line. This movement is accomplished so that your body moves completely together and everything stops (hands, feet) at the same time. Things that I work on while doing this are making sure my balance doesn't go forward (ie. leaning forward) or backward while moving. The feeling throughout should be the same as kamae, except that the back leg is out further so you are lower, however you still have your front knee over your front toe and your belt over your heel. I also practice suriashi (sliding) so that my front foot rises as fast as my back foot pushes so that I slide across the mat and don't step. I push off the back foot to get power going forward. My arms lead from their elbows in a circle up, which pushes my hand up with my back leg hand further forward than my other hand because I use that hip to push my body straight. By practicing all this together in one basic movement we should be able to make our technique stronger whenever we need to move in a straight line.
Hiriki no yosei ichi with partner extends what is practiced when doing it by yourself in two ways.
1. As uke you learn to move with shite. This will help you to be an uke and improve your understanding of the way techniques work
2. As shite you will learn how to keep contact with uke and how to move them when there is no resistance and when there is lots of resistance. In both cases you are learning how you can affect uke's balance through a single point of contact, so that while you are moving from one point to another strongly forward in a single line you are also moving uke with you to that next point.
If we look at how the whole "with partner" thing works...
1. Shite / Uke face each other in kamae
2. Shite / Uke shuffle forward. Uke has the front hand out to guard against shite's front hand. After the initial shuffle, uke is close enough to cross-step in and grasp shite's wrist with both hands like a baseball bat while the now back leg shuffles to the side. Uke should now be facing shite about 25 degrees off shite's front arm to the side
3. Shite shuffles forward do the strongest hiriki no yosei ichi that they possibly can.
4. AND this is where the question comes in where the two things I study with partner (as I mentioned above) come into play.
A) Learning about uke
As shite moves forward uke moves with them exactly, sliding backwards at exactly the same pace, but being moved by shite. Uke slides back and having their arm pushed up in a circle to lock it into the shoulder. Uke should keep focus between shite's eyes, while shite should keep focus directly ahead. When shite moves back, uke should again move with shite back to the original position, again keeping focus between uke's eyes and both shite/uke should end up in a strong kamae (knee over toe, belt over heel, etc...)
While this is happening you should be able to feel how shite's contact with your hand stays the same or how it changes to make the circle go up. You should also feel that your reaction is a microsecond behind shite (inertia...a body at rest tends to remain at rest) so that it is the start of their motion that you respond to. As uke you learn not to move in a direction other than what shite is moving you and not to move quicker or ahead of shite (since this could have bad results in jiyuwaza or any technique)
B) Learning about shite and moving uke
With little or no resistance you should be able to feel the continuous pressure of uke's hands on your forearm. Since uke is moving with you on purpose and is not resisting they will help you understand where you should move them to because they basically put themselves there.
If uke resists (by maintaining their kamae) then shite's challenge is not to lose any of that form or touch that you aim to practice when do hiriki no yosei ichi by yourself. The hardest part here is that as you try to move forward you may find that your foot comes off the ground and moves forward, but your arms and body stay where they are. Another common problem is that your arms lose the basic kamae shape (and therefor the strength from that) and move back into your body pushing your shoulders up.
To get around this you have to find the point of uke's resistance and then go around it (short answer to your question). To do this I suggest keeping your body together by not reaching forward with your front foot and by not letting your arm's kamae shape collapse. Do this by moving your knee forward. This will drop your weight slightly and if you don't lose your arm kamae shape, it will bring your elbows in a line under where uke is resisting. So...you've found the point of resistance and gone slightly underneath it. Now you can push off with your back foot to move your body from one point to another. You are going from under their point of resistance kind of parallel for a brief moment. From their you can hook your wrist/baby fingers up (as they do in hiriki no yosei ichi) and this will cause you to circle up around the other side of uke's point of resistance. Here your back foot and your kamae shaped arm with the elbows pushing forward supply the power. You have gotten underneath (slightly) uke's point of resistance and then up the other side. Uke should actually feel a huge circular motion around the shoulder. This is where you have to feel the contact that uke has with your arm and move with it so that uke cannot let go. I usually aim for the middle of the V in each of uke's hands.
When you return to kamae with resistance you you have to make sure that circle you used to bring uke's shoulder up and locked is used to snap them back into kamae in the original position. Here you push back with your front foot, keep your kamae shaped arm, make sure your armpits are "closed" and your shoulders down and maintain your balance all the way through. Uke should feel a snap back to their original kamae. Here you should also work on the contact so uke would find it difficult to let go. Here you would be pushing against uke's baby finger and their grasp. Since they are resisting and hence grabbing strongly this should work.
I think when you saw Shioda Sensei driving through uke he was probably finding that point under the resistance mark and then up around it. If he were driving through then uke would probably end up moving straight back staying in kamae (assuming a strong kamae) or not moving at all (if uke were heavier than him).
Sorry for the long post but as I said we've been studying this pretty intensely over the past two weeks, so it all just keeps on coming out <g>.
If anything doesn't make any sense or seems just plain wrong, please let me know. I'd also be interested in hearing what (if anything) I suggested is the same/contradictory/new to you.