I did some digging into the Trilinos reinit_matrix, and I've found that all 
of my lost time is coming from the operation

  graph->FillComplete(input_col_map, input_row_map)

This step is accounting for as much as 20 seconds per call for a 1x200,000 
matrix on 4 processors. I also found that this bottleneck is non-existent 
running in serial. There is a check earlier in reinit_matrix which calls 
graph.reset differently for 1 processor vs. multiple processors. The 
comments suggest that there's an explicit reason for treating the mpi case 
this way, but that treatment seems to be causing the problem for my case.

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