Could an amateur build a full-scale UAV?
You sure can, 

The FAA provides a special airworthy cert for this kind of thing. There are a few types that you can apply for depending on what you are trying to fly. You can find the relevant info here 

You can find the full Special Order that covers it here.


  Airworthiness Certification of Unmanned Aircraft Systems and Optionally
  Piloted Aircraft 
  
  
  Purpose of This Order. This order establishes procedures for issuing special airworthiness certificates in the experimental
  category or special flight permits to unmanned aircraft systems (UAS)
  and manned aircraft integrated with UAS technology. For the purposes
  of this directive, manned aircraft integrated with UAS technology are
  referred to as optionally piloted aircraft (OPA).
  


In your specific example if it was an RV-8 (built as it usually is) with the ability to remote pilot it added in, it would be classified as an "optionally piloted aircraft"