The attack was shomenuchi, in the cutting forward and down style, not the cutting forward only style you sometimes see. The technique seemed to be both linear and circular...linear in the intial entry into uke's space, circular in that you body changed to what would now be the back knee down, circular again in the way you matched uke's arm and cut out and down.
I have tried similar techniques when uke attacks with a bokken...it does liven things up a bit, and it also seems uke extends more...there is a wider distance for them to cover and shite can take advantage of that. In the technique in question, it was interesting in trying to deal with many different body types and attacks. We weren't dealing with one uke...it was hikari geiko, so you had a line of about 10 or so attackers, and had to adjust to each attack accordingly. I also found it distracting not to be sure of the ukemi level of each attacker...there were a few people who might not have liked the rough rider version of the throw.
I agree with your latest assessment...surprise and a very commited uke make the technique/exercise work...and the same with what you called leg takedown. I've found that lifting my balance to the point where my shoulders rise is a good setup for that throw...uke see you go up, they go up, and then you enter into the hole they leave. Of course, if they don't respond as expected, you are kind of open to a whole bunch of things, the easiest being a simple thrust kick.
As they say, timing is everything.