This is what I ended up doing to split the single-table dump into one file per row, named by ID:
awk -F',' '/^INSERT/{print > gensub(".*\\(","", "G", $15)".sql"}' ../big.sql
Where my table has around 15 fields. This takes the 15th column, separated by "," and replaces out the remaining SQL part (there are more elegant ways to do this, works only because I have numeric-only identifiers)
This is full script - I happen to have only one such table, so it misses the logic of the other answer
#!/bin/bash
DBNAME=example
BIGTABLE=big
mysqldump $DBNAME --single-transaction --quick --complete-insert --skip-extended-insert --ignore-table=$DBNAME.$BIG | sed -e 's/DEFINER[ ]*=[ ]*[^*]*\*/\*/' > sql/master.sql
rm -rf sql/master.d
mkdir sql/master.d
mysqldump $DBNAME --hex-blob --single-transaction --quick --complete-insert --skip-extended-insert $BIG | sed -e 's/DEFINER[ ]*=[ ]*[^*]*\*/\*/' > sql/master.d/$BIG.sql
cd sql/master.d/
mkdir $BIG.d
cd $BIG.d
awk -F',' '/^INSERT/{print > gensub(".*\\(","", "G", $15)".sql"}' ../$BIG.sql
rm ../$BIG.sql