Users expect submit buttons to be at the end of forms, and users utilizing screen reading software face greater issues when they are located elsewhere.
It may be possible to add additional submit buttons that are only readable by screen readers at the end of forms to accommodate users that require screen reading software.
Example: Patron Search form Search & Clear Form buttons
The buttons are in the middle of the form instead of at the end of the form. They are read directly after the middle name field, so if the user is just searching by name it is fine, but if the user goes beyond the name fields to search by barcode or username or some other field, it is not clear how to get back to the search field.
Example: Patron Edit form Save and Save & Clone buttons
The buttons are in line before the form fields begin, and since the autofocus goes to the first open field, when the user completes the form, there isn't a Save button at the bottom, and they have to either cycle through all of the other page elements first or search for the button using their navigation search tools.
I have tested the patron edit form using the NVDA and I can confirm the problem.
Beside the issue described by Terran I have also found, that when jumping by the active elements of the screen (fields, links etc.) using TAB key or screen reader shortcut in the Patron Edit form interface, the Copy/Print links related to the Mailing address in the "Patron summary display" appear between the "Save & clone" button and the "OPAC/Staff Client User Name" field. It is confusing by my opinion as the user don't know, what are the Copy/Print links related to. It would be at least useful to add the title to both links, to inform the user that those links are related to the Mailing address.