Which heritage conservation program? You should probably ask them if recreated birds would be counted.
With chickens, phenotype is often as important as genotype.
Genotype is the genetic makeup of the bird. Phenotype is what you see, when you look at the bird.
If a cross between a Barred Rock and a New Hampshire produces a bird that meets the SOP for the Delaware breed - that bird IS a Delaware. The SOP -the phenotype- defines whether or not the bird is a Delaware.
If you are going to be breeding Delawares, the genotype is important.
If you have multiple lines or breeds (a broad mixture of genes), your breeding results will vary widely. The results will be less offspring that are phenotypical Delawares.
Actually, even breeding poor quality Delawares can produce similar results. If the results don't meet the standard for the breed, then the offspring are not Delawares, no matter what you used to produce them.
So, the best way to produce true Delawares in the most consistent way, long term, would be to breed Delawares with phenotype and common genotype.
JMO ... Once the majority of the offspring that you are producing are close to the SOP for the Delaware breed, you can count yourself as a Delaware breeder.