Can one reverse a hash with partial plaintext knowledge? First off, please forgive my ignorance because I am not as well versed in cryptography and mathematics as I would like to be. I may say something obviously wrong/dumb; please point it out!

Is there any technique which may reduce the difficulty of recovering plain text from a hash if the attacker knows part of the plain text?

Here is an example.
Alice writes this letter:

Dear Bob,
   Run!
Yours Truly,
Alice


Alice sends the plaintext to Bob over channel X and the hash over channel Y.

Eve intercepts the hash but not the plaintext.

Eve knows Alice starts the message with "Dear Bob," and ends with "Yours Truly, Alice".
Eve also knows that Alice sends messages in fixed blocks and will pad the body content with whitespace to meet the required block length.

Can Eve use her knowledge of 1)fixed message size and 2)partial plaintext knowledge to reduce the computational difficulty of reversing the hash?

I would appreciate any help on this topic, even if your answer is just "read this whitepaper".
For an ideal hash function, the fastest way to compute a first or second preimage is through a brute-force attack. That is, if there's no structural weaknesses in the design of the hash function, your best bet is to mount a brute-force attack.

The knowledge of the message size (n bits) and some parts of it (m bits) will certainly reduce the complexity of finding a preimage under the brute force attack: The worst-case complexity will reduce from 2n to 2n-m. 

A space-time trade-off over the brute-force attack is by exploiting rainbow tables. I believe  the partial knowledge of the preimage may prove useful in mounting this attack too.