I don't have JMP 11 installed anymore. but you can check. See Help > Books > Predictive and Specialized Modeling. There should be a chapter devoted to the Fit Curve platform, right before the chapter about the Nonlinear platform. If not, then JMP 11 did not include this recently added platform.
I think that the GLM could be modified with cross terms (interaction effects) to test some of the hypotheses. For example, in determining expiry, time is crossed with batch to test poolability. If this term is found to be significant, then a unique slope (degradation path) is required for each batch. If not, then a common slope can be used.