TakingTerns,
Let me allay some of your fears regarding towing a TM with the Jeep Liberty. We spent the last two winters (Jan, Feb, Mar) in southwest AZ, CA, GA, FL, SC, and NC. Our 2004 Jeep Liberty Sport did just fine. From our home we traveled I-84, I-81, I-40, I-20, I-10 to reach the Tucson area. The trip back to the east coast was a little easier as we stayed on I-10 one year and drove I-20 to the Atlanta area last year. If you are interested, we had a travel Web site for our 2005 trip and it is still open for viewing.
http://mytripjournal.com/trailmanoradventure2004-2005
When deciding which TM you can safely tow don't forget to check the manufacturers recommended trailer length. I believe the Jeep Liberty has TT length limit somewhere around 20 feet. That would put you over the limit if towing the 3124 model.