Your question states that this eugenics endeavor is one of inbreeding, and that is the fastest way to maximize the prevalence of the traits that you want.
"Interestingly, before the advent of genetic testing for recessive traits the only way to statistically ensure genetic “purity” of a bull/ram/buck etc. was to breed that bull to 35 of his own daughters concurrently. If no genetic defects show up in any of the offspring, the bull is 99.7% likely to be genetic defect free."
Your project will require a lot of incest and a lot of culling.
I found this interesting; from http://bowlingsite.mcf.com/genetics/inbreeding.html as regards all matings being brother - sister crosses:
"The figure shows how the inbreeding coefficient chages with generations of brother-sister matings. As a general rule, this type of mating in domestic animals cannot be kept up beyond 8-10 generations, as by that time the rate of breeding success is very low. However, the rare survivors may go on to found genetically uniform populations..."
Thinking strategically you might not want to commit the entirety of your breeding population to the project because your population will crash because of inherited diseases. If there are any survivors after that crash those could be your super soldiers.
I can imagine that these super soldiers are a religious project of the society: breeding brother to sister, culling the unfit etc. The end result of your super soldier project would be that your super soldiers and their sisters / wives will be genetically identical: a stable lineage free of inherited diseases with predictable characteristics generation after generation, just like an inbred strain of lab mice.
This super soldier thing proposed here is grounded in genetics but is appropriate only for a work of fiction. The bowling site article notes that the ultimate phenotype of a stably inbred strain has a lot to do with luck and that it is very difficult to control exactly which genes these stable strains has. So the prospect of actually pulling off a breeding experiment like this in real life (human or otherwise) seems slim. If it could be done it would be a great thing for popular dog and cat breeds; the fact that these breeds still suffer from genetic diseases suggests to me it is not an easy thing.