Entropy would take a serious hit if you did that.

Not necessarily. If only one-fourth of all English words are grammatical after an average prefix, then you lose two bits of entropy off each word after the first. I suspect that the actual situation is not as bad as that. You might end up using "uncommon" words like "deceased", "advent", "fearful", and "ram" to compensate, instead of more common words like "strongly", "contains", "afterwards", and "corporate", but that doesn't seem like a major loss to me.

Any narrowing of the search space will most definetely reduce entropy.. by how much is calculatable but I don't have the time nor language statistics right now to do it.

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.

> I'm not sure the technical meaning of entropy in this context

Roughly, it's the logarithm (base 2) of the number of guesses that an optimal password guesser would have to guess in order to guess your password. It's a measure of how unknown your password is.

> it has so many possible combinations, that every speaker is continually creating sentences that have never before been uttered.

Yes, this is why all of the suggested alternatives like "choose a line from a popular song" are so much less secure.

You can modify slightly your sentence without loosing entropy

"married greatly snake battle" becomes "a married great snake will battle".

"correct horse battery staple" becomes "correctly the horse inserted the battery staple"

Note that the extra words add little or no entropy, at the cost of increased length.

This is a good idea!

You do lose a little entropy that way: you've merged "great" and "greatly", and "correct" and "correctly", suggesting that your modification process considers adjectives and their corresponding adverbs as equivalent. If those examples are typical, that removes one bit of entropy. But you've probably added more than that back in, if your choices of "a", "will", "the", and especially "inserted" are unpredictable. (Alternatives might include "the", "would/did/could", "a", and "removed".)

For what it's worth, Google finds more hits for "fearful" than for "afterwards" and more for "ram" than for "corporate". ("Strongly" and "contains" do beat "deceased" and "advent", though. And yes, many of the hits for "ram" are really for "RAM".)

My frequencies are from this word frequency list from the British National Corpus: http://canonical.org/~kragen/sw/wordlist