I do have some bulky items i am trying to upgrade slowly but I think the shape of the main compartment doesn't help me either as it tapers in at the top of the bag. I agree with the 3-4 days out of this bag(it would be tight) but I am wanting to eventually get to the 7-10 day trip length .
I looked up the Badlands Ox to confirm what your working with and everything I read puts it at 3234 cubic in (53L) and over 9lbs 6 oz for pack and frame. If your doing 4 days out of that now, then any bag from one of the top manufacturers in the 5500 cu in range or higher will be an incredible upgrade for you. I personally run a mystery ranch beartooth 80 for long hunts and a MR Pintler for short ones. The beartooth does strap down very tight for day use as well and runs great without its lid to reduce bulk as well. Great system.