I agree with previous comments that the AIF is not a suitable way to extract large amounts of data from AX, but for the sake of completeness, I have seen this issue before and we found a couple of quick workarounds:
1. Be a system administrator in AX
2. Modify a macro value defined in the AX code
Option 1: The problem is caused by a permissions issue. There is a method: AxdBaseRead\findLimitOnDocument() which looks up the details of the outbound port setup when creating the outbound message. If the user doesn't have permissions to read that setup (where you specified the max document limit) then the method will use a macro value which is hard coded.. Which leads to option 2:
The 1000 record limit you are hitting is specified as a macro, which is defined in the class declaration of the AxdBaseRead class.
You can increase the limit here, do X++ and CIL compile and the issue goes away:
#define.MaxNumberOfDocuments(100000)