The oustanding share count (or, better, the fully diluted share count) should be used for all "valuation" metrics such as EPS. Float is relevant only to market issues like trading, spread, availability of shares, etc.
I'll buy your .20 projection, as it is based on outstanding shares. We can tweak the assumptions, or the values used, but that equation is valid in form.
Since the $1.75 figure was derived using float as share count, it is meaningless to me.