I'm not sure the technical meaning of entropy in this context, but personally, I would offset the narrowing effect of "restrict to grammatical phrases" by adding uncommon words. "Besotted ophthalmoscopes gambol indicatively" forms a coherent, if silly, word picture for me, so I think I can remember it.
As far as possible combinations, my vague memories of linguistics 1001 include the idea that this is one of the essential properties of language: it has so many possible combinations, that every speaker is continually creating sentences that have never before been uttered. Unlike, say, honey bee dances, which are often repeated.