I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
A judge is prohibited from practicing law while he is on the bench, even for clients he helped before becoming a judge, so he should not be preparing anything. It's a violation of the Code of Judicial Conduct.
With that said, if you sign the quitclaim deed, it is valid. A person should never, ever, ever sign something they do not agree with. In a divorce, property is evaluated based on current market value, not based on what the parties paid or the tax assessment. Tax assessments are almost always lower than what a house is worth, because the city doesn't want to spend a lot of time and money valuing everyone's upgrades to their home. They're basically assuming all houses are in bad condition when valuing them for tax purposes (more accurately, they're saying, "The house is worth at least this much...").
It is possible to sign the agreement and have it notarized while in the Air Force, but again, that is something you'd only do if you agree with it. You're allowed to ask that they redo it, using the correct fair market value of the property.