I would think that the heart of your problem lies in surface area of the tire touching. If you are running narrow tri ribs, then there really isn't much surface area touching. If you change to wide front tires, then that will help with your turning/gripping.
Another possibility is to just lay a sandbag/bag of water softener salt over the front hood, being careful not to obstruct/touch your exhaust or dent in your hood.
WARNING: I HAVE NEVER TRIED THIS NEXT METHOD. I JUST THOUGHT OF IT
AND IT MAY NOT WORK LOGISTICALLY, SO TRY IT AT YOUR OWN DISCRETION.
This one depends on your fabrication skills. You could also get some threaded rod to replace your bolts that hold your front rims on--1/2" (?). Put your wheels/rims on, washer, threaded rod followed by two nuts to hold rim in place. Then fabricate a 1" diameter rod (6-8" long) with tapped thread O.C. at one end and a hole drilled in the cross section of rod, about 1/2" from other end of the rod for a lynch pin. Screw the fabricated rod onto the threaded rod that you cut to length. Then you can buy/find barbell weights from the store or find in a garage sale--the little 5 lbs. weights would be ideal because they are thinner than the plastic, sand filled ones. You should be able to put about 5 or 6 on each rim.
Cub Cadet 123