Do you have your seat far enough back? If you are back far enough, the weight on your hands will decrease, you will be more balanced. You will be able to take your hands off the bars without falling forward. It doesn't take a big difference to accomplish this.

I will still say I had to drop the height slightly with my Brooks. Once I did it was extremely comfortable and no more pain in the soft parts. Mine is not laced. There is a slight possibility that the lacing is actually making matters worse for you since it makes the saddle flex less. This may be contributing to the pain in the soft parts.