So there is a little "trick" that I left out. The steps to scale to absolute lengths would be:
Select everything you want to scale
Select the scale Tool
Scale the selection from one corner - don't worry about the size at this time. The Measurements box will not become available until you do this.
After scaling, type in the dimensions including the units - 10",10",6" - and press Enter
Because inches uses the " as the suffix,you need to use the Shift key, but the Shift key resets the Measurements box. This is why you need to go ahead and scale to an arbitrary size first, and enter the absolute lengths afterward.
If you were using mm, then you could grab one corner, begin to scale, and before completing the scale operation, you could enter the lengths: 3mm,3mm,3mm (for example.)