Can you negotiate with Palm Harbor for their homes, like you can for other real estate, or are the prices set?

Everything in real estate is negotiable and never let anyone tell you otherwise.

The trick is (1) understanding if the market is seller or buyer dominated and (2) how to determine "mush-y-ness" in the numbers.

The current market is almost all up to the buyer (a buyer's market), meaning you generally have the upper hand.

Mush-y-ness is a little harder to define -- It is where, exactly, the person you are negotiating is flexible. You need a general sense of how eager they are to sell -- but keep in mind they are professional sales people, you are not. Even if they are desperate to sell you may not know it unless you do your homework. (And that's part of the reason you hire a good buyer's agent -- they are excellent industry spies). Some builders, for example, will not budge on the price of a unit or house, but will give away the rest of the business for nothing: upgrades, cash, loans, etc.