The system you're describing is woefully vague. What are the dominant genes that respond to the recessive? Are you describing only one particular gene, or just the total gene pool? Are we to understand that these are negative effects that significantly affect the ability to survive and breed? Do the positive genes significantly increase the ability to survive and breed?
A single trait does not have two different recessive genes that code for something. One possible gene will be dominant and one will be recessive (clearly I'm simplifying this to a simple two-gene trait for the purpose of the argument).
Let's try a thought experiment in a standard society where excessive inbreeding does not occur. We will look at a negative gene that causes infant mortality, and a positive gene that prevents infant mortality. These are the possibilities.
Dom= good, Rec=bad
People will survive if they have even one Dom gene, but die if they have two Rec genes. Since anyone with one Dom and one Rec will survive and reproduce without knowing they have the Rec gene, the Rec gene will survive in the population. Inbreeding, working how it works, will cause instances of the Rec gene to increase, causing more children who will die from the defect.
Dom=bad, Rec=good
People will survive if they have two Rec genes, but will die if they have even one Dom. Anyone with the Dom gene will die, preventing them from surviving and breeding. Therefore, the population will quickly have only the Rec gene. Incest is unnecessary to increase instances of the Rec gene since natural selection has already selected against the negative Dom gene.
As demonstrated through the thought experiment, inbreeding is unnecessary to promote the prevalence of positive recessive genes. Natural selection already does that. Additionally, incest can only serve to increase negative or inconsequential recessive genes. That's as simple an explanation of human genetics as I can give.
Addition: Just realized I could add an example like Sickle Cell Anemia where a DomRec will prevent future disease
So now, Dom=good, Rec=bad, DomRec=best
People will survive if they have even one Dom gene, but they die if they have two Rec genes. However, people with both a Dom gene and a Rec gene will live and breed longer than someone with two Doms, because they have an added immunity to some disease (we'll just say influenza). You have a similar situation as "Dom=bad, Rec=good," except the Rec gene will be more pervasive in society since it does, occasionally, provide a benefit. In this case, inbreeding will lead to more people with two Dom genes, or two Rec genes. This is bad for society since it minimizes the maximum number of healthy people. Ideally, if you are DomRec, you want to breed with a DomDom, because, statistically, 0% of your children will suffer infant mortality, and 50% will be resistant to influenza.
Now I know what you're thinking. "Now they have 50% of their children DomDom, and 50% DomRec. Clearly those children should reproduce in order to maximize the next generation's gene-pool. However, in this scenario we're assuming that there's no way to tell who has what genes. You could easily pair up DomRec with DomRec, and then a quarter of their children would die. A gene like this is very unfortunate, which is why Sickle Cell Anemia is such a problem. However, inbreeding is not the solution. The best solution is for carriers of the Rec gene to outbreed as much as possible in order to avoid other carriers, while still possibly spreading the flu resistance. And yes, if they're carrier's, the best place to find other carriers is in their own family.