Your above spoiler tag won't open for me, so I'm not seeing what A.N.B.E. stands for. However, one thing you may have miscalculated -- or perhaps not -- is the time it would take to get the Constitution-class from design sketches to completion. Not the Enterprise herself, but -- and this is an assumption, because we don't yet know what all has been jettisoned, what's been kept and what's transitioned from fanon to canon, which may occur in this film. Typically, a class of ship is named after the first vessel constructed in the class, which would be the U.S.S. Constitution. Maybe you see where I'm going with this. If the Constitution was already completed when the Kelvin is destroyed -- or if even the design is finalized when the Kelvin is destroyed -- then your theory won't fit.
"Now I did a job -- and got nothin' but trouble since I did it, not to mention more than a few unkind words as regard to my character, so let me make this abundantly clear: I do the job... and then I get paid. Go run your little world."