In terms of creating a space-saving reading system, I think a better place to start would be with the writing system itself. Dotsies squishes letters but does not remove them.
I propose a system where each word is reduced to its minimal representation, eg. where letters are removed until the smallest unique form is found (giving more common words shorter forms).
Once I have such a mapping developed (for both reading and accelerated writing) I will see if something like dotsies still makes sense.
In any case I will not use squares: they make my eyes sad. Maybe circles :)