Welcome to FT, Sunny. Unfortunately, I expect that these are like money orders which have similar phraseology. The "Not to Exceed $1,000" is probably pre-printed on the form, the intent being that if over $1,000 is required, a different form (presumably with additional/different approvals) must be used. If there's no other mention of an amount, you may have been given a blank one. I would call AA before you do anything. Ask them about the form, how it's supposed to be filled out, etc. Without being deceptive, try to avoid identifying yourself. Then, perhaps, reassess after you have the info from AA.
Maybe even come back here, report and ask for further suggestions!! One thing FTers are not short on is suggestions on what to do!!!