Yes, JMP can handle the mixture amount approach. You specify your mixture components as ranging from 0 to 1. Add the mixture amount as a continuous variable with the appropriate levels. The model would then be a combined mixture-process variable type of model since you have a non-mixture factor along with the mixture components. Once the design is created you can then create the additional columns that specify what the true component ranges are for the mixture components, based on the total mixture amount.
There may be a few additions needed, such as linear constraints in order to ensure the actual component ranges match what you can achieve, but this is certainly possible.
Alternatively, you could use JMP to take the Component Amount approach that Piepel demonstrates. That approach may be a bit more straight-forward. This paper outlines how you could do either one, and JMP can help with either approach.
Dan Obermiller