Yes, you may have used too much wood for the smoke, even though it does not take long for the steaks to reach temp. When I have done steaks, I use red oak but only about 1oz and they taste great. You might also want to remove the steaks a bit earlier, let rest foiled while you fire up the grill, and then grill to your desire temp. Just another way to try this out, but I think you will like the results.
Steve