Flying *Through* DC

While doing some preliminary planning for a June trip from KLOU to
KWWD ( Cape May, NJ), my "direct" path would take me right over the
center of DC ( in the Prohibited area).

I have reviewed the articles and AOPA advice on travelling in and
arround the ADIZ, and know the procedures. Most of that advice seems
to be focused around navigating through it - but only on a North-South
axis.

Any ideas on how to plan? A northerly or southerly transition ? It's
all busy space...

Thanks