Since there don't seem to be any, I'm looking for a full sized one with backlight and that it has larger keys and/or wider spacing between them than the above CM Storm.
I am confused, do you want the numpad or not? You can get an mx brown keyboard in just about any config you want. You can even get the CM Storm Quickfire TK with mx browns. Just search amazon for mx brown.
Ideally it would be the same configuration as the QuickFire TK above, but if there aren't any a normal one would be ok, but it needs to have larger keys and/or spacing between them than the QuickFire. I don't have a place to try them so I'm looking for some recommendations from people that know a certain model that fits the criteria.
Keycap size and switch spacing is pretty standard among all commercial boards. You are going to have a hard time finding anything with non-standard oversize keys or wider spacing. Maybe search stores that specialize in goods for people with disabilities? Or keyboards for children?
The other options would be to build your own custom board.
Yeah, size and spacing seem to be standard. I like the TK as it is both smaller and still has both the arrow keys and numpad, although not at the same time. I do find that I make much more typos compared to my old membrane keyboard (currently have a O ring modded red version), hence the search for a different key size/spacing one.