Hi Centaurus,
I can't speak for your 737 sim, but when we did simulated EFTOs (idle thrust on OB engine selected) on B707 during base training, then it needed more NU trim than a normal all engine climb out.
Your logic with "If the airworthiness certification of the simulator stab trim forces means in-trim at V2+15 with two engines then I can understand that following a engine cut at V1 and the decision is made to continue, the absence of the failed engine to provide a vertical component of thrust as the nose rises, will give the effect of a nose heavy aircraft that requires significant stab trim aft to get back into trim."
is correct.
How much extra nose up trim does it require to fly 15 kts slower?
I suggest if you doubled that (for the loss of the nose up couple from the failed engine) - then you'd be about right.