Yes, sorry. You need to overwrite the initial value (H0) too, in the constructor. You can do that if you can touch the equivalent of the private member variables.

    SHA-512/256 may be used to hash a message, M, having a length of 𝓁 bits, where 128 0 ≤ 𝓁 < 2.
    The algorithm is defined in the exact same manner as SHA-512 (Sec. 6.4), with the following two exceptions:
    1. The initial hash value, H(0), shall be set as specified in Sec. 5.3.6.2; and
    2. The 256-bit message digest is obtained by truncating the final hash value, H(N), to its left-most 256 bits.

(from §6.7 in http://csrc.nist.gov/publications/fips/fips180-4/fips-180-4....)

EDIT: I trust 'tptacek (in sibling comment) that if there is no chance of protocol confusion, there is no advantage to the different initial value.