"like I wasn't present with the shot...." Very good description of body awareness (or lack thereof). You can, and should, develop the same level of awareness with the lighter bow. In fact, you should strive to increase your level of awareness with all your bows throughout your shooting life. Your lighter bow will allow you, in time, to feel minor muscle movements that you can't feel with the heavier bow. Your shooting with all bows will improve as a result.
The only downside is that your lighter bow will eventually begin to feel normal to you, and your heavier bow will feel too heavy, so be sure to put in some time shooting the heavy bow before you hunt with it. It shouldn't take too much time before it starts feeling normal again.