The main thing that I would be concerned about would be relationship structure in the BC1F2 population: batches of individuals with closer relationships among individuals within batches than between batches. This can lead to inflated LOD scores.
karl
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I like your idea, of using the 4-way cross, for handling the allele frequency issue. But I'd do it as the next generation. You just need genotypes on the BC1 parents.
karl