Using factor analysis to avoid Bonferroni death?

I have a study with three dichotomous IVs and five DVs, which are brief, relatively reliable composite scales derived through factor analysis. If I run 2x2x2 ANOVAs for each of the individual subscales, I get great results, with interactions supporting my hypothesis. However, if I use a Bonferroni correction or run a MANOVA, only the main effects are significant and I lose the interactions. My question is this – Are factor analytically derived scales sufficiently independent that it is no longer necessary to correct for Type 1 error? I have seen allusions to this on the Internet, but can’t find anything authoritative in Gorsuch or other sources. Alternatively, is there a less conservative correction that is appropriate in this case? Any suggestions would be helpful!