When it comes to this whole "lining up" idea, the real light bulb moment for me came with kouchi and ouchi gari. First, let's talk about the way I was taught kouchi gari.
As my right foot goes back, I move it a little to the side and turn it inward (toes pointed at uke). I bring my left foot next to it, heels more or less touching, toes pointed out so my feet look like a "V". As uke's right foot comes forward, my left shoots out and catches the heel just as it's about to touch. I push the foot further forward than uke intended, and he falls.
Very little, if anything, was ever mentioned about what the hands are doing. Which is probably fine, when teaching it to new students. The foot work is tricky enough to figure out, just because tori has to do 2 motions in the time it takes uke to do 1.
Now, bare in mind this approach works pretty darn well. I've used it for a long time, and have had great success with it, and many folks have used it on me successfully, too. But since I don't have uke's hips and shoulders lined up with his feet, however, I occasionally found that he had an easier time countering my kouchi with hiza guruma if I was even just a little bit off.
Clif Norgaard Sensei once instructed me to get in closer, let the bodies connect, and sort of "bump" uke's center with mine, essentially displacing it. Over time, I played with that idea, and eventually it led me to a slightly different entry.
I still pre-turned by right foot as I stepped back, but not off to the side as before. Now, it's more straight back. As uke's right foot becomes airborne, and as I quickly slip my left foot behind my right, heel to heel, I do the elbow draw I mentioned in earlier posts. This puts his hips and shoulders are in line with his feet, we have close contact, his shoulders are a bit back over his heels, and I'm throwing him perpendicular to the line of his feet:
Even if I botch the timing, because my center is now occupying the same space that his center wanted to occupy, and because he's on his heels, he can't remain standing up anymore anyway (and a hiza counter, at least, is virtually impossible).
Although, the real fun came when I realized that this helped me do kouchi gari advancing. For some reason, no one has ever talked much about doing many judo throws advancing, at least not in my experience, so I've had to figure it out mostly on my own.
For this, I simply turn my right foot, toes inward, as I step forward. Immediately, I bring my left foot up to meet it, heel to heel, doing the elbow draw with my left hand. Here, the elbow draw not only turns uke's hips and shoulder in line with his feet, but it also tends to stall his right foot and keep it from traveling backward. Now I'm square to him, perpendicular to his line, and he's on his heels (our bodies connected). From here, I can shoot in for not only kouchi gari, but ouchi gari as well.