Oh ye of little faith.

unshuffle.c

uint64_t shuffle(uint64_t state)
{
    uint64_t word = ((state >> ((state >> 59u) + 5u)) ^ state)
                    * 12605985483714917081ull;
    return (word >> 43u) ^ word;
}

uint64_t unxorshift(uint64_t xs, uint32_t shamt)
{
    // bits:
    // xs[i] = x[i] ^ x[i+shamt]
    // recover one by one, higher bits to low
    uint64_t x = xs;
    uint64_t bitmask;
    for (bitmask = 1ull << (63 - shamt); bitmask; bitmask >>= 1)
        x ^= (x >> shamt) & bitmask;
    return x;
}

uint64_t unshuffle(uint64_t shuffled)
{
    uint64_t word = shuffled;
    word = unxorshift(word, 43u);
    word *= 15009553638781119849ull; // modular inverse
    word = unxorshift(word, (word >> 59u) + 5u);
    return word;
}