Thanks for reaching out George! Honestly, I don't see a reason why this ammo should damage a *reproduction* 1903A3, but that's not enough to make a promise which could wind up damaging your rifle. I always defer to a firearm's manufacturer's opinion when it comes to ammo compatibility. I just sent an email to U.S. Armament Corp asking for their take on the matter, and I'll relay their input to you as soon as I hear back from them.
*UPDATE* I just heard back from the gunsmith at U.S. Armament Corp. He said that this ammo is indeed suitable for your rifle!