ft,
This is sounding to me a bit like an undergrad mini-thesis exercise ? Might we know the task purpose, if that be not confidential ?
The sort of things you appear to be after would probably require the assistance of the engine manufacturer's data package and that is unlikely to be forthcoming for other than an airframe manufacturer.
Apart from that, the only option I could see would be to make a first pass model from AFM and planning data. Acceleration data could prove a difficulty to resolve but you might be able to get some in-service data from a helpful operator and then try to massage that into some sort of order.