reasonable doubt has nothing to do with this case

this is not a criminal case. the standard is "more probable than not". So if jury thinks that there is a more than 50% chance that infringement occurred, you are liable.

the only way to convince the jury is to dispute the truthfulness of the records. if all you can provide are circumstantial evidence and unstantantiated testimony, i would think twice about the settlement offer.

you can try to negotiate with their lawyer on your own, and see if they are willing to lower the settlement value.