I agree with 826ih regarding the flatdeck Towtruck. As for the trailer aspect a tilt/load car hauler that is rated for 10k should also be capable of the weight.
But many car haulers are only 7k and as such the real max load on it should be less than 5k as the trailer would weigh 2k or more. Mine is about 2200lbs with a full steel deck plus the weight of the winch/battery and any tiedown gear. Hind sight is 20/20, ...wish I had bought a 10k tilt load trailer. But this is fine for me for now, ...just have to keep in mind my load weights for vehicles, ... technichally I can't haul complete full size trucks, ..especially 4x4's due to weight. my 03 1/2ton Sierra ext cab 4x4 weighs 5520 last trip on the scales as an example. That would be overweight for the suspension rating of the trailer with dual 3500lb axles. Now a 2wd the trailer should be fine, ...just have to make sure I have the hauler truck licensed for the weight as well, lol, more isk to the gov't coffers
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