Customer claims electronic transfer is the wrong amount. Our records indicate the transaction was authorized and completed online. Customer has not provided us with any statement as to what the correct amount should be or a copy of her billing showing the correct amount. It's a health clinic and I'm sure if I contact the clinic for verification of billing amount, they will not provide me any information.
Would my investigation be complete if I can show the amount authorized and debited are the same, and state we see no error, or how much further do I need to take it, or am I just out $704.60? Transaction amount was $754.60

You researched your records and found no error. End of story.

Unless the customer can provide you with what she believes to be the correct amount, you really have gone farther than you needed to. But if she does provide that amount, your investigation will have to include whatever you can get by way of confirmation from the clinic. You are entitled under card association rules to request a copy of the authorization ticket (sales draft copy request).