While Colorado had the best idea I tried a few others first, and it worked.
I removed the top plate (#17 above) and that gave me more room to get at the blockage.
I started from below and moved what I could with a thin but sturdy piece of wire and then flicked out the remainder blocking the top one at a time until I couldn't see anymore from the top. Gave it all a blast of air from a can and dirt and crud all came tumbling out.
Very nervously sent a spent primer down from the top and was very relived to hear it hit the floor.
Thanks All!