Specific use of verb 'to plow through'

I have the following sentence:

I seemed to recall meeting her while she was plowing through books reading.

I think this is wrong. One way I would fix this would be by adding a comma before ‘reading’:

I seemed to recall meeting her while she was plowing through books, reading.

Or I would just remove ‘reading’ altogether:

I seemed to recall meeting her while she was plowing through books.

Which correction would be the best to use? Or is the original one already correct?

This question ultimately concerns the usage of ‘plowing through books’ since in my understanding, it means to go through books by reading them. If this is the actual usage then it would make ‘reading’ redundant.