I don't really know how to do this in Audacity ; I was using it a bit for a while but kind of put it on the back burnder. I'm trying to learn Reaper, but the learning curve is a bit steep. I could accomplish this using Goldwave. There is a trim silence feature you can use, and aside from that, you could always just find an appropriate place in the file and just repaste appropriately as needed. I think there are several ways to accomplish this and, maybe you'll have to get creative. If Audacity doesn't have a functino to automatically trim silence, or if it does but it still isn't to your liking (entirely possible), you'll have to edit manually. I have done this before as well but, it's been a while.
Sorry if this isn't too helpful, but, given the tools that you have, you should be able to accomplish something satisfactory. Someone more familiar with Audacity should certainly chime in.