Each of the Hawkeye rifles responds differently to floating, bedding and increased forearm pressure. Here's an old trick that might help you decide what your rifle needs.
Cut up an old plastic credit card. Make 3 shims: one for the flat just behind the diagonal bedding screw, another for around the rear triggerguard screw, and the last to increase forearm pressure (this one may require several layers).
Fire 3-5 rounds with the rifle stock to get a baseline target.
Install the first two shims (this simulates floating the barrel). Fire another 3-5 rounds. Compare this group to the baseline target. If the group-size gets larger, then floating your rifle won't improve accuracy.
Remove the first two shims and install the forearm shim to increase tip pressure. Fire another 3-5 rounds, and again compare to the baseline.
Usually one of the configurations will give better results than the others. That gives you an indication what your rifle likes.
Ted