I did what @Wrikken suggested. I deleted my table and lowered varchar's max_length attributes to 1500 from 3000. I then ran this SQL on my new empty table
ALTER TABLE `table_name` CONVERT TO CHARACTER SET utf8 COLLATE utf8_general_ci;
from here, I repopulated it with my backup table, using a script.
To answer the question: Lower varchar max_length limits Or change varchar fields to LONGTEXT, or BLOBS