I think you misunderstood my "spinning helplessly" comment. Spinning helplessly does not automatically mean spinning at an uncontrolled / high speed, the tires may well be spinning at the same controlled speed as the front tires, but with no traction they are still spinning helplessly and all the traction load is on the weaker front axle. Indeed with no load in back and no high speed spinning, the rear tires are that much more likely to cake up with packed snow and have zero traction. At least the occasional high speed spin may clear the packed snow from the tires.
The front axle is virtually always weaker than the rear due to the additional universal joint required on the steer axle. Having all the traction load on the front axle due to snow pack and insufficient weight on the rear axle, combined with intermittent traction shock loading greatly increases the probability of damage to the front drive train, be it to the hubs, universal joint, CV joints, axle shafts, differential, etc.
If you only have one set of chains, put them on the rear. Get some weight on the rear as well, even if you have to just shovel snow in the bed, anything will help.
Pete C.