If you are performing full-page recognition via processPage or processDocument calls, you can get this information in xml output. The coordinates of recognized characters are output in original image's coordinates. So you need to determine the similar text areas on different pages and compare their coordinates.
You are performing field-level recognition via processTextField. In your case this can't be done in single step since you need to know exact positions of different fields. After the page is recognized via processImage or processDocument, its subsequent recognition via any method including processFields will be free. So, you need to perform processImage or processDocument to xml, determine coordinates of the fields, then do processTextField for the same file, and it will be free.
However, to avoid service abuse we implemented a limitation on free pages per day. There are 300 free pages per application per day. After this amount all the subsequent rerecognitions will be billed.
Another issue is document rotation. In processImage/Document it is corrected automatically. In process*Field case we cannot do that because otherwise all the coordinates user passed us will become invalid.
Right now I don't see elegant solution to your problem. So all your suggestions are welcome.