There could be a workaround to achieve your goal by following the steps below:
1) Create a new web app such as IndexApp, and copy the bin folder from your web app into this one.
2) Create an UltimateSearchInclude folder under the root of IndexApp.
3) Move the Admin folder from the UltimateSearchInclude folder of your original app to the UltimateSearchInclude folder of IndexApp.
4) On IIS, right-click on IndexApp/UltimateSearchInclude and create a virtual directory called Index and point it to the physical folder of the UltimateSearchInclude\Index directory of your original app. Do the same for the Log directory.
Now you can set up any port you wish for your IndexApp. Whenever you open the admin page, and index your app, it should generate the index and log files under your original app.