I was taught a throw in Muay Thai of all things, which they just call a "foot sweep," but I recognized it as a Judo throw. It is shown at 2:20 in the video linked below. It could be mistaken for one of the "ashi" throws in Judo, except that Uke's leg is not actually swept. The leg has weight on it, and Tori just blocks it from moving. The throw is accomplished not by moving Uke's leg, but by shifting this body over the blocked leg. I'd like to know the proper name of that throw.
The judo name is sasae tsurikomi ashi (propping, lifting-pulling leg). Your mechanics description matches this quite well. Done in a minimalist judo style, the leg is not kicked, but simply blocked.
To make my comment into an answer:
What you describe and the coach in the video explains is sasae-tsuri-komi-ashi: You block the forward foot and add a lifting and twisting movement to their front in order to have them eventually release the building tension into a breakfall.
What they actually do in real-time execution, though, is going into the opponent, moving so that their center of gravity is under theirs, and sweep. That is a different throwing mechanics and thus a different throw: harai-tsuri-komi-ashi.
It is also not a hiza-guruma since you would have to position differently in order to block at the knee: you have to stand at the side of the opponent, not in front of them.
The reasons that this has to be labelled as harai-tsuri-komi-ashi are
- Hip contact
- Front positioning
- The leg is, in real-time, swept and not blocked. The thrower moves through without a stop. If he blocked, there would be an ever so slight stop of the leg movement at the moment of contact.
I agree with the previous suggestions Sasae-tsurikomi-ashi and Harai-tsurikomi-ashi, and I'd like to add Hiza-guruma into the mix.
In Hiza-guruma, the blocked leg is not the front one, but rather the back one. Tori blocks uke's knee (hiza), unbalances and tilts (guruma=wheel) uke sideways over the blocking leg.
Well, they are very similar looking, but method of throwing differs on each.