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This doesn't quite answer your question, because we don't really do much beta testing of documents here, but it does address the broader topic of how to get feedback from the field.
I have set up a "Technical Documentation" email address and listed it in all of our technical manuals. It is designed to be used for unstructured feedback (reporting of errors, omissions, and any suggestions). That seems to work pretty well in terms of getting some feedback. Customers don't use it much, but our internal field service engineers and system installers do.
I don't think people use paper and the mail for this kind of thing anymore. You might be more successful if you could get the names/phone numbers of the beta test customers, call them, and complete the survey over the phone. That way, they do not need to take the initiative or make much of an effort.
Susan Jelus
Senior Technical Writer
Thermo Fisher Scientific
Logan, Utah
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