Ok, some thoughts...
What happens if the interaction disconnects part-way through? How does the servicing application know to enter a disposition phase?
Is the servicing application both a) web-based and b) developed in-house? (I suspect from your question, the answer to the latter is "yes", or at least you have control over it.)
If so, I would have the developers write the servicing application "client" as the script. In other words, the agents access the application through Scripter. That way, you can have tight integration between Dialer and your application.
If the answer is a) No and b) yes, then I would again look at a single client-application. That is what ICELib is for. Adding the Dialer/ PureConnect pieces to your existing application shouldn't be a big job and will probably, in the long run, be less complicated and more supportable than trying to customize both the servicing application and the script so that they talk to each other.
Just my 10 cents.