Barons destroying the berserk packs are the biggest issue for me, which is why I aim to pursue and kill them outside the center building, instead of trying to camp there for them. I avoid the Arena Master blowing them up by using the strategy I mentioned to deal with him.
To pick up the Chainsaw with a full inventory, if your hands are empty, you can hit the use button over it and that will pick it up. You can also do that to pick up any weapon, armor, and boots from the ground and equip them instantly without them going into your inventory, as long as the corresponding equip slot for them is empty.
By camping in the central area waiting for the Arena Master as I described, you'll be able to avoid Formers getting in there when you need to get to a Berserk, while also limiting the amount of distance you need to go to run away from him (which reduces damage and decreases the chance of him blowing up the Berserk as you get to it).