I don't use the snake roll with the long-belly lines because I find it takes too much effort to aerialize the line on the initial forward roll of the line, which is especially noticealbe when using a sink tip.
Alas, I have no video equipment so I don't have the capability of getting a video of long-belly casting.
I also agree that we are talking about doing the same thing with using the lower hand push to help accelarate the line into the D Loop. The point at which we add the lower hand push might be slightly different, or the amount of lower hand used may be slightly different; but it really is the same thing. The only reason I mentioned the lower hand push was you had left it out of your initial post.