There's only 1 seat available unfortunately, which is the problem with UA. My fault for not double checking....no luck on the YYZ-ADD flight either.

There is KLM/KQ space - IAD-AMS-NBO-LUN, but I wouldn't do it because of the fees.

If you're willing to waste some time in transit, it's easy to leave on the night of the 29th - to ADD on 30th - ADD-LUN on 31st. Without much difficulty I found IAD-MUC-MXP-ADD-LUN. If you're willing to do something like that, there's a ton of availability.