Hmmm, thinking back on one of the first batches of soap I made, I remember leaving it in the mold (cardboard box lined with freezer paper) for a coupld of days because it seemed soft to me. When I did unmold and cut it, it was firm, but like a cold block of Velveeta, it cut very easly and stayed soft enough to press a fingertip into for a couple of weeks.
And recently I made my coffee soap, and put some into an empty plastic tub from a flavored cream cheese spread and even though I left it almost a week, it was still too soft when I lost patience and unmolded it anyways. Not to the point of what she was doing in the video, but I could have easily molded it into a ball.
Before I made a single batch I read everything I could get my hands on through my local library. I'm sure I remember some of the soapers mentioning that sometimes it took three or four days before the soap would be firm enough to unmold and cut, so I can see where this could be doable if you have a recipe that stays soft for a while, especially if it's put into a Ziploc so the water can't evaporate out right away.
A wild thought, liquid soap paste can be pretty thick, maybe you could use a combination of soaps? Sort of like doing a croap--aren't some of those pretty pliable?