Hi Tom, and welcome to the BrickWood forum.
Both things are true. You get the best mix with a mechanical mixer, especially considering that you have a relatively large quantity of a heavy material that has to be mixed all at once. And, the mechanical action of the materials mixing comes with a good amount of friction, which heats up the mix and shortens the “window” for casting to a point where you might have trouble.
So, take your inspiration in a tall, cold drink of water. Measure out the water for the mix in one of your 5-gallon buckets, and mix with plenty of ice. The heat generated by the castable will be absorbed by the ice-cold water, thus extending your casting time enough that you can work with it.
Hope this helps, and hope we’ll see you often around here. Good luck!