The number would be a bit bigger starting from 46 ft. since you are using a smaller distance to start with, however typically speeds thrown by 12yo at 46 ft. are proportionally lower so you'd get roughly the same result I did.
The math works out pretty simply. I assumed a release at 54 ft. from the plate and a release at 53 ft. from the plate. You can then take about 1/53 of the velocity to get the apparent change in velocity. For the result to be a change of 3 mph the average velocity would have to be about 160 mph. I think that may be a few years away.
As far as the difference between reaction time and velocity approaching the plate let's go back to the LL vs MLB example. A 70 mph fastball thrown from a 46' mound will reach the plate in the same amount of time as a 91 mph thrown from a MLB mound so the reaction times are the same for the two pitches. I've simplified this by using the mound distances rather than the release distances but the result is essentially the same.
The 91 mph fastball, on the gun, approaches the plate at about 82 or 83 mph. The 70 mph fastball approaches the plate at about 64 mph. Reaction times are the same, but I'd find it a lot easier to hit the ball moving at 64 mph than the ball moving at 83 mph and I think the same goes for most people not playing pro ball. If I practice I can hit that 70 mph fastball from 46'. I could practice all I want and I could never get around on a 91 mph fastball thrown by a pitcher from a 60'6" mound. The easiest way to tell the difference is to put on the gear and try catching them. That 70 mph fastball from 46' is catchable for an old duffer like me. The 91 mph fastball from 60'6" would be just plain dangerous, gear or not.
I don't know how many times I've seen coaches throwing to players at half the distance from the mound at 40+ mph and the kids just hammer it. Yet the same kids can't catch up with an 80 mph fastball thrown from the mound to save their lives.
In essence one has to fully commit to the swing when the ball is further from the plate if the ball is moving faster as it approaches the plate. That is not directly related to reaction time as you can see from the LL vs MLB example. The ball speed as it approaches the plate when the ball isn't in exactly the location you are expecting is one reason why bat quickness is so important and why sluggers like Dave Kingman who had great bat speed but not quickness struck out so often.
Now if you take two pitchers throwing the ball at the same speed at release and one is releasing a foot closer to the plate then there will be a small change in reaction time which we've seen isn't that important and a much smaller change in the speed of the ball as it approaches the plate. The difference is about 1/8 mph. That is virtually meaningless considering the relative speeds of the bat and ball.