Entropy in natural language texts
Shannon's paper Prediction and Entropy of Printed English details  the experiment to determine the entropy of English.
Without getting into too much detail, it's only really proper to talk about the entropy of a source of information. You can estimate the entropy given a sample of the source's output and it's fair to say that Shannon's method gives an estimate for the upper bound. A more sophisticated experiment would give a lower estimate for the upper bound.
Another way to arrive at an upper bound would be to look at the results of a competition to compress a portion of wikipedia which shows that 100M of English can be compressed into 16M.

I'm reminded of a similar scheme I read about which relied on a long stream of publicly available bits derived in this case from digitizing a picture of the surface of the moon. I can't find the reference but I'm sure it would be relevant, although of purely academic interest.

There are no practical schemes that I am aware of which use your idea or anything similar. You would have to ask yourself what security guarantees you're trying to achieve and whether this really is the best way of obtaining them. I believe that it should always be preferable to implement your system using established cryptographic primitives in the prescribed fashion.