How hard is it to certify a kit aircraft if it is based on a production design like a Cessna 180?
The FAA requires all aircraft above a certain weight (>ultralight) to be certified. You can certify the design and production process so that everything that comes out of the factory has a guaranteed level of safety, or you can certify the result. The former gets a standard certificate, the latter gets a special airworthiness certificate. Other jurisdictions make similar distinctions, with minor variations.

Kit planes, such as your 180 replica, get a special airworthiness - amateur built certificate. FAA AC 20-27G outlines the process for satisfying this requirement. It is sixty pages of instructions, limitations and forms. The two most commonly mentioned requirements are for majority construction by the amateur and for flight testing.


  It is important to document the entire fabrication and assembly process from the beginning to the end, in a continuous and sequential manner. This is because, at the time of certification, the FAA is required to ascertain whether the amateur builder(s) fabricated and assembled the major portion of the aircraft. Making this finding requires adequate, sufficient, and credible documentation.


For flight testing


It does not matter to the FAA whether or not it was based on some production certified aircraft. 


  We do not certify amateur-built aircraft designs or require that you modify the design before airworthiness certification. However, we may deny airworthiness certification when we inspect your aircraft if we find it does not meet the requirements for the certification you request or is not in a condition for safe operation.


This is far less stringent that the requirements for a standard certificate. You will have to decide whether you consider this "a large amount of testing".