Handling a big table in mysql
I'd suggest a more radical approach. For databases of your size a fulltext search is not only ineffective, but inefficient. I'm guessing that there's some kind of user-driven search function requiring your index.

How about you employ a real search engine? This would take the load of key generation and reordering off of your database. It would give you the chance to offload the load to even another machine.

Take a look at Apache Solr, a well-received, fast implementation based on Lucene. Many large non-profit and commercial websites use it with success.

Then, remove the fulltext indexing from your table. Inserts should then fly into the table with only the ID key left.

Also, if you regularily remove rows from the table, OPTIMIZE TABLE should be done regularily.

For backup purposes, you might consider replication. There are multiple ways to implement the replication, and all of them spread the load out over time, instead of creating a downtime for it, which is what you have now. As an added benefit some replications can produce a database that can be used as a stand-in replacement if the primary database fails, so that the application can be up again in little to no time.