My lease specified that I must give 60 days notice before I vacate, which is fine, but 59 days before my lease is up, I received a form from the complex stating that my notice will not be recognized unless I use the form given.

I don't want to use the form given because it adds additional terms that I don't want to agree to that were not in the lease. For instance, this form states that I will not get ANY of my security deposit back if I do not comply with all of the terms of my lease. Well, I believe that generally a complex can only keep that portion of your deposit that covers their actual damages incurred as a result of your breaching the lease, so I do not want to agree that if they incur $5 worth of damages, they can keep my entire $300 deposit. Furthermore, the form they provided requires that you provide your work number and reason for moving, neither of which I find to be relevant or any of the complex's business. Lastly, it states that I agree that they may show my apartment 7 days per week between 9 and 5, which I feel is excessive.

Can such a requirement be legally upheld?

The provisions in the lease will prevail.

Unless this "form" is listed as a term of the lease, no they can not enforce it. But this is what will happen, they will enforce it, and you will then have to sue them in court for your money, providing them with a copy of your legal notice you have given them, a copy of the lease and so on.

I would also personally send them official noice, certified mail, that their notice does not meet the terms of the state law or the lease agreement, and that you will not be able to use it, unless proper changes are made.
And also show that in court as proof you (asked) for a new form that did not have any new provisions but were refused one.

Hello the:

I would also add that they may show the apartment at anytime during those hours, however only WITH 24 hour notice.

excon