Both Hilton AND Sofitel "allow" you to get back to your car in the morning - being allowed is not the issue, the issue is that (unless things have changed over the past year, which I doubt) NEITHER have parking on-site. So you be in the same boat if you stay at EITHER the Sofitel or the Hilton... both will require 30/45+ minutes (probably more - depending how lucky you are at catching buses) to drop your cot/bag off at your car.
I know that when we used to stay at the Renaissance, their parking was on-site at the hotel. Although that was a few years ago (haven't stayed there in at leats five year, but probably more like 7) - so their parkinf situation may have changed AND have heard some bad reports about the Renaissance (gone downhill apparently...). Moat House also has/had parking on-site at the hotel, but I was incredibly unimpressed by botht he hotel and the parking and REALLY wouldn't recommend it...
There may be other hotels with parking on-site at the hotel - maybe someone else can share their experiences.
Personally I would ask the Sofitel to provide the cot and follow Obi's advice...
Alice