Longitude of the Ecliptic
There's a mistake in the book (see page 280 on google books): the values for $\lambda_{ecl}$ and $\phi_{ecl}$ should be swapped. Your result is correct:
$$
-6338.688^\circ\text{ mod } (360^\circ) = -218.688^\circ,
$$
which is the value that is erroneously listed under $\phi_{ecl}$.