We have a chest freezer packed to the top. Digging around for stuff, I take stuff out and put it on a shelf, or even on the floor.
I feel your pain. We had chest freezers when I was growing up and I hated it every time mom sent me to get something. This is the exact reason I bought a huge upright. It was $1200 brand new at Sears outlet store and I got it "scratch and dent" (ever so slightly) for $400. Well worth it to me.
Robert