Have it looked over by a trusted shop or dealer, maybe do some of the minor maintenance like serpentine belt, hoses, plugs, fuel & air filters. Inspection of brakes, tires, and running gear of course. I highly recommend a transmission service, and possibly a cooler upgrade. Google 6.0 transmission cooler mod. Maybe get a 2nd serp belt to carry with.
If you trust the EX daily, you shouldn't be wary of a cross country towing trip.
Our '03 has approx 109K on the odometer, and has done a 5000 mile trip back to the midwest towing our almost 7K Jayco, many 3-10 day mini-vacations in the mountains of WA and Oregon on many fairly steep passes. And will be going down to the Utah/Arizona area for a 30+ day trip in mid Feb. I don't have any worries about it doing the trip. I run Mobil 1 5W30, and change every 7500 miles or at 6 months. Maybe use 1/2 quart in summer towing between changes.
If your V10 has been maintained, and kept up with, it should be good for many, many more miles.