My advice would be that when you play a Pet Steelclaw you're telegraphing your intentions pretty clearly, and putting all your eggs in one basket. Your opponents can probably avoid one Bear for quite a while. A Pet Steelclaw with Bear Strength costs 27 mana, 28 with Ring of Beasts, too. Even though Ring of Beasts + Double Steelclaw costs slightly more at 34, it has a higher damage output and is far more durable and resistant to disruption.
If your opponents are playing living creatures mostly, consider playing a Dire Wolf book. You can get a Ring of Beasts and three Dire Wolves for 35 mana (which, again, is slightly more) but they are quite scarey if you're aggressive with them. If your opponent is guarding with non-living or otherwise very tough creatures, use Teleport to bring his or her Mage to your Wolves' zone, and use Bear Strength on the Wolves as opportunities allow.