I have been looking for a piece of software or webpage that works like
this: you input a body of text (typically written by a certain
author), and the program statistically analyzes this text, then
outputs a new hunk of text which resembles the input text's style,
word choices/combinations, etc.

Find me such a program!

So, just to clarify, you want to be able to input a block of text by,
say, William F. Buckley, and then you could type in, say, "I drank the
Coca Cola," and you'd get out, "I ingested the caramel-colored,
caffeinated, carbonated beverage known by its inimitable and
indubitably famous moniker, Coca Cola, which, by the way, was in turn
inspired by its original formulation using coca leaves, the source of
cocaine (C17H21NO4)."  Or you could enter a block of text by, say,
Ernest Hemingway, and then you could type in, say, "In rapture I
watched the multi-hued sun retreat behind billowy clouds and willowy
wisps of trees.  Night encroached upon me, and peace was my reward,"
and you'd get out, "I watched the sun set.  It had been a good day."

Hmmm.  Why do you need software?  It's pretty fun just to do it yourself. :)

Haha :)

What you describe is close to what I'm looking for, except for the bit
about "translate my provided sentence into another style".  Rather,
the program just needs to take a block of input text, and then
statistically generate a "random" output text which uses the same
kinds of words, word patterns, and puncutation which the input-text
already contains.  Although if you could find something that could
actually "restyle" a sentence based on the input text that would be
quite incredible.

A typical use might be to collect several dozen articles from a given
author on the net, and run it through this program to 'randomly'
produce an output text which, while it might not make coherent sense,
would still resemble the author's use of word
choices/patterns/punctuation since it was wholly derived from the
input text.  Presumably hitting the "generate output" button
repeatedly would spin different permutations of that input text.

The interest I have is in generating such an output text from a given
author's provided input text, and seeing how difficult it is to then
ascertain that the output text was not in fact written by the author.