Yeah single axle is not to even be considered but even with two 3500# axles, it's so easy to go over with an average CUT and implements.
There have been several threads just recently with guys asking if they are within safe operating specs with 7K car haulers, and it's always right at the borderline, either a little over or barely under.
It's a constant worry, with the load a half inch one way or another, one of the axles is overloaded.
10 K trailer is the way to go, harder to find a deal on one but worth the effort of getting one, will always be worth decent money for resale as long as it's rolling.
JB.