Interesting topic that doesn't get a lot of coverage. I recently copied a little over 5TB from my raid server to my HTPC over wired gigabit LAN connection. My RAID array can pump out about 850gbps so I was able to sustain about 100Mbps transfer rate to the HTPC that I had just installed 3 new 3TB drives combined into a single 8.5TB storage pool. That's probably as good as it gets over internal wired gigabit lan.
In your case you are looking at copying 2TB or less onto an external drive. It all comes down to speed. If you're connecting over eSATA, USB 2.0, or USB 3.0 it will all come down to the speed of each drive and the link between them as the slowest of the 3 will determine how long it takes. The fastest method would be to remove the 3TB drive from the enclosure and connect it to an internal SATA port, but the time saved may not be worth the effort. It all depends on where the weakest link is. USB 2.0 caps out at about 30 Mbps, so you can do the math to figure out how long it will take to transfer all your data. 30MBps sounds pretty fast until you do some math and realiz that it's going to take about 35 sec/GB x 1000/60 or about 10 hours per TB. Installing the drive on an open internal SATA port and getting 100MBps brings you down to 3 - 4 hours. Obviously, the more data the more time savings can be had by getting a faster connection. Also keep in mind that some hard drives can't sustain 100MBps transfer rate so even when you get the best connection you still won't exceed the max capability of the slowest drive.
In my case it took me a little over 16 hours to transfer 5TB @ 100MBps
The days of sitting down and actually planning how, when, and where to best manage big data are now coming to the home network in a big way that most users have never thought about before. Another reason why there's such a push to convince everyone to move to the cloud as most users won't be interested in managing their own data this way. That, and of course they all want to lock you up as a customer for life once you've surrendered all your data to the cloud where the government can hack into it.
I'm not too sure about your podcast issue as I've not tested it in Madsonic, but I would think you should be fine moving what you have and redefining the location. Hopefully MadEvil can chime in and confirm.