Are you suggesting a very large custom blocksize? I don't think this would be feasible beyond a few megabytes.

No, a FPE algorithm is a cryptographic construct that uses an existing block cipher (e.g. AES-256) to construct a cryptographically secure permutation of the input without length extension. That is, input size = output size, for all sizes. Ideally, if input size >= block size of the underlying cipher, the resulting permutation is no weaker than just using the cipher directly.

You could use FPE for multi-megabyte permutations, but I don't know why you would.