I see no reason to mix by hand, I just throw in my cups of salt and throw the drill stirer at it and voila, mixed and airate in under a min
Also, I had the preciptate when I just had a heater in a bucket and let it sit overnight or sometimes longer, but I was using a broken heater that would take the temp to about 84.
Anyways...
give it a try and see, try mixing when it is cold and then throw the heater in and heat it to tank temp.
Also, you do not want to make a super concentrated mix, in other words, you take a bucket and fill it up with 5 gals of water and then proceed to dump say 5 cups of salt, then you try to mix it and add more water till your up to the correct S.G. . If you do it this way you are asking to have percipitate problems