Thanks for all of the responses. I ended up purchasing a 2007 Explorer V8 and picked up the trailer last weekend. I bought a weight distributing hitch and added a sway bar to the set up. The brake controller I purchased was a fancy pants Tekonsha model.
The drive home was 450 miles, with the roads being in good shape for the entire trip and a mix of 2 lane and 4 + lane highways. The trailer pulled very nicely and even with 18 wheelers passing close and some wind on Sunday, I didn't feel any sway. The braking was very easy to adapt to. I can see where a trailer that was a bit larger or heavier (or significant inclines) might present a problem for the Explorer, but I felt comfortable going from West Texas to Houston, except for the gasoline stops. Those did scare me some.
Here's a picture of the trailer and Explorer (before adding clip on mirrors).