we are talking about technology base that is able to build Capital ships in weeks, and Executor Class vessels in Months. If construction was started shortly after Ep II that means they had 3 years by the time we see the DS Skeleton in Ep III. If Construction of the second Death Star started soon after ANH, that means it took less then 4 years to build "a fully armed and operational battle station"
so I think it is quite possible for a Death star skeleton to be constructed in a few years
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get busy with it!