You could get away with 4awg, yes. But if you plan to upgrade to anything larger in the future, you might as well run 1/0 now.
The distro block you listed is not a good choice for you. Find a FUSED distro block and get that instead. To figure out the size of fuses you need.. is easy. If you end up going with 4awg, the main fuse should be no more or less than the capacity that the wire can handle. so for 4awg the suggested fusing point is 150A. For the distro fuses, I would assume you're splitting the 4awg to two 8awg lines (I would still go with 1/0awg), fuse each split at 80A.
The "adding up the fuses on the amps" is totally the wrong way to fuse. You fuse to protect the wire from bursting into flames should a short occur. Most amps pull far more than the rated outside fuses anyway at full bore. So the adding method would be completely useless.