To the best of my knowledge, the ISTD has never included the Alternative Basic Movement as a figure in Cha Cha. They only do this in Rumba. I cannot speak for the IDTA, Guy Howard, or any others.
Of course, that doesn't mean that such a figure doesn't exist. It just means you can't dance it during your ISTD exam, or during a syllabus-based closed dance competition. But for all other circumstances -- why not? If it's something you like to do, do it!
As for the various types of chasse (eg Compact, Ronde, Twist, Slip, etc), these are not actual figures. They are basic components -- building blocks, if you will -- from which figures are comprised.
The following are examples of basic elements: The forward check, the back break, and the basic chasse. If you put these elements together in the right order, you can form a figure known as the Cha Cha Basic Movement. Add some rotation in the right places, and you can also use the same elements to form New Yorkers, Hand to Hand, Shoulder to Shoulder, and others.
So the Chasses that you listed are nothing more than basic elements which go into the figures listed in the syllabus. Some of these elements are fundamental to the figure; Others are alternatives to a more basic version. For example, a standard side chasse is considered to be a basic element of the man's part of the figure known as 'Hockey Stick'. But in place of the standard side chasse, he can also dance a compact chasse, a slip chasse, or a ronde chasse (although the latter is considered to be more advanced, and may be restriced to higher levels). Whichever type of chasse he choses to dance, he's still dancing the figure known as 'Hockey Stick'.
Regards,
Jonathan Atkinson
