What is the next best law school for DC?
Besides GW and GULC it could be Howard.
If OP was a URM this would be credited, but it doesn't appear that he is. Howard's appeal is that its OCI rivals GW and GULC's, rather than looking like American or Catholic's. But, and this is key, the reason it's so large is that employers go there hoping to find good diversity candidates, and a white person at Howard just doesn't fit that bill.
OP, if you want DC Biglaw, your best bet after GW is probably W&M. HOWEVER, I would never, ever advise anyone to go to W&M if DC biglaw was their first choice. Your chances of actually getting that kind of job from that school are extremely low. Don't go to Emory/Fordham if you want DC. I haven't met a single biglaw attorney from either of those schools out here; past the T-14 (and even that's debatable) it's all regional, and those schools aren't in the region.
If you can't get into GW, I'd either wait a cycle and retake or rethink my career goals.
This isn't advice I give often, or lightly. But as someone who went through GW's OCI and watched a lot of people end up disappointed, I can't in good faith recommend you spend money hoping for DC biglaw at a place with worse prospects.