Probably the easiest way is to do a pocket query of the area of interest, then import into a desktop application, such as Garmin BaseCamp (Windows or Mac). From there go File > Import into my collection (runs out of memory with 18000 caches, so choose a smaller number). Then go View > Swap Map and Data Views then click on the Placed By column header to sort by owner.
Not that this is the placed by field, not the owner field, but in most cases this will match.
In the end I wrote an Excel script that does a much better job of importing and displaying geocache data (to help determine if I qualify for challenge cache before geocheckers came out), you are welcome to it, send me your email address in a geocaching message and I can send it to you.
Just realised you asked for user id, not user name. This data is not included in a gpx file, so the above method will not work. I suspect the only solutions for used ID are hard.