Your approach is generally correct but the devil is in the details. Unwarranted differencing can lead to very spurious results. Ignoring anomalies (pulses/seasonal pulses,level shifts and local time trends can be the downfall of a tf model. Changes in parameters over time or changes in error variance over time need to be investigated. I am afraid that both SAS and R are not up to these challenges. You might post your data or send it to me at my email address and I will try and answer your specific questions and post an analysis to the web. If your data is confidential then we can do this off line although I would prefer to enlighten others as to what can be done.
In closing ... it is generally speaking not a good idea to use percentages but rather use both observed series when constructing a model. Care should be taken to distinguish between trend and level shift activity as most software including JMP can not detect time trend changes which is precisely what you are looking for. Some software (JMP in particular) assume that both the parameters and the error variance are constant over time. Be wary of such simplistic solutions as they are often wrong and need remedial treatment. it is interesting to me that SAS's defaults for JMP is to NOT detect level shifts. I wonder why ?