
If you are impressed by the yellow mutation of the cut-throat then you can introgress the character into the red-headed finch. Sinedel (1986) mentions this was the same method that was used to move the colour mutations between scaly to the rainbow lorikeets.
At least in the case of cut-throats and red-headed finches it seems that hybrids form a substantial part of the wild population where they over-lap according to Tarboton so their distinct specific designation is moot. In Australia we commonly see intergrades between rosella species. Given the imperilled gene-pool of the of the redheaded finch in Australia a touch of cut-throat might just be be what is needed to save it rather than destroy it.
Is hybridisation harmful to genetic integrity? There is no correct answer as each aviculturist's goals are subjective, not objective - nature intends nothing but it is a fact that only the fittest survive. As was demonstrated recently in mimetic South American butterflies, the capacity to be able to introgess colour pattern from "unrelated" species through hybridisation can be actively selected for because it is desirable in some circumstances. The creation of novelty through mutation, hybridisation and shifts in gene frequencies in population occur over time and allows a species to adapt and survive. Do the most "pure" of aviculturists bemoan the fact that Gouldians are no-longer the fragile tropical birds that they once were? I seriously doubt they do but show them a colour mutation and it's rejected. If the yellow-headed mutation had shown up first in the aviary rather than the field would it too be despised? I'm sure aviculturists will break up into the usual camps of mutant-lovers and purists over this too. So is preserving diversity OK only if the allele occurs spontaneously and becomes fixed in natural populations in the period 1800-2012? I don't have an answer for this but I'm sure everyone has an opinion.