How to limit undesired traits in "breeding-back"?

Modern “breeding-back” projects such as Taurus cattle and the Auerrind project work with a breed selection that comprises all achievable morphologic aurochs traits. Size, proportions, colour, horn shape and size and body morphology to a certain degree. But the problem is that the sets of breeds also include a lot of undesired traits. Recessive colour variants, as well as alleles for very small horns (which might be recessive too, see here) and for different horn shapes. It requires a lot of breeding work to purge those unwanted traits from the population. Recessive alleles in particular are very difficult to breed out. While it is well-possible to achieve very good animals with the sets of breeds chosen, it will be difficult and longsome to truly stabilize the breed for the traits desired because of the high number of undesired traits. 
Therefore, I have been making some thoughts on a project that minimizes the amount of undesired traits but still is able to achieve all the aurochs traits that are achievable with domestic cattle. 
 
Such a project would have to chose breeds that already resemble the aurochs to a large degree and do not have any undesired recessive colour variants or different horn shapes or sizes. I think that a combination of wildtype-coloured Lidia, Maronesa and Sayaguesa would be suitable for this purpose. Lidia would contribute a very aurochs-like body morphology, Maronesa has the sexual dimorphism and horn shape (in good individuals) and Sayaguesa would contribute large size, long snouts (at least in cows) and long legs. The horn shape of this combination would be good to very good, no deviant colour variants would be present and since some Sayaguesa grow up to 170 cm withers height the right size would also be found in the gene pool. The bulls might end up a bit short-legged, however, and the horn size might not be that impressive, but overall it would be possible to breed a good result quite fast and would be a lot easier to stabilize. I would love to see Lidia x Maronesa, Lidia x Sayaguesa or Sayaguesa x (Lidia x Maronesa).