I have always been able to find space in the "economy" lot.

http://www.mwaa.com/national/dcapark.pdf

It is much smaller than it was in the past, and slow down, there is only one entrance and it is easy to miss.

Getting from the lot to the plane station seems to take forever. I did not time it, but I think I could have walked faster.

I do not know of any long term off site parking. The Sun lot is gone.