The Export link in the Table view brings up the export sub-panel for a specific table. It is similar to the database export panel, but there is no table selector. However, there is an additional section for split exports before the Save as file sub-panel.
The Dump 3 row(s) starting at record # 0 dialog enables us to split the file into chunks. Depending on the exact row size, we can experiment with various values for the number of rows to find how many rows can be put in a single export file before the memory or execution time limits are hit in the web server. We could then use names like book00.sql and book01.sql for our export files.