You're overthinking it. First, the A3 sight can't fit on an '03 without a lot of work. Secondly, an 03A3 barrel will fit an '03 receiver. They're the same, minus the relief cuts for the staking pins for the rear sight sleeve, which can be added. Just beware that 03A3 barrel quality was all over the map 74 years ago, and hasn't gotten any better in the meantime. There's a reason pre-war '03 barrels are sought after and it's not all for "collectibility" reasons.
Were it me, and I have done it twice now, I would shell out $200 for a new Criterion '03 barrel from the CMP. They're made by a division of Krieger. They come short chambered and already Parkerized, with all sight cuts done. A couple twists of a chamber reamer brought mine up to minimum headspace. Accuracy is about what one would expect from a pre-War star-gauged '03 barrel which is to say excellent- and they're allowed at the vintage service rifle matches at Camp Perry.
Getting the sight sleeve off of your old barrel is not a task for the faint of heart but it can be done. On the other hand, wartime '03 replacement sleeves are still floating around and wouldn't add much to the cost of the job.
Most service rifle competitions require the use of the service sight, or sometimes optics (as on sniper rifles).
Last edited by gnoahhh; 08/01/16.