Each share is (roughly) the same size as the original. In effect, all of them are just encrypted versions of the original.
For some reason, my gut was telling me each piece would be smaller than the original.
I wonder if this (horcruxes of size ~ 1/N) is actually possible.
If your data is compressible, you should do that first.
In particular, consider your example (5 horcruxes with 3 needed to reconstruct). View the original file as the interval (0, N) and view it as a set covering problem. If each horcrux covers an interval of size N/3, then if any pair overlaps, there is no third horcrux that can complete the covering. This is a contradiction because 5 horcruxes of size N/3 must overlap somewhere.
RAID 6 uses some linear algebra to allow m of n copies to reconstruct the original data, where typically m = n - 2, but the math works for any number you like. So if you split up the data using the exact same algorithm, and pre- or post-encrypt the blocks, you should get the same thing being attempted here, and only inflate storage by n/m