Shiny ... so a flatbed is substantially more than the U-haul? I'm not familiar with local rates ... my 1100 miles trip the U-haul cost $700.
I found the trailer brakes to work very well. The trailer they gave me was a tank, and in very good condition. They weigh every bit of 2000 lbs.
Do you know what rear end is in the truck? I wouldn't think 70 miles would present any problem at all unless they are all uphill, or any really steep grades.
The trailer was all of 2 feet wider than my GTO, has to be a foot wider than your truck.
Here is a link to the specs of their auto trailer:
https://www.uhaul.com/Trailers/Auto-...ort-Rental/AT/
I had absolutely zero sway of any kind. I had several butt puckering moments on the trip and the trailer behaved beautifully, it was more composed than I was.
For only 70 miles I wouldn't hesitate, go as slow as you want. If it's only $150 more to hire a flatbed ... I personally would go with the flatbed, mostly just to avoid trailer pickup, drop-off, loading, unloading.