InnoDB files created even innodb_file_per_table is OFF in mysql-5.7
Not matter what you configure innodb_file_per_table to be (0 or 1), the following still occurs

MySQL creates a database folder
MySQL creates every table's .frm in a database folder

EXAMPLE
Your database directory (datadir) is /var/lib/mysql
You run the following commands
CREATE DATABASE IF NOT EXISTS mydb;
USE mydb
CREATE TABLE tb1 (a INT NOT NULL) ENGINE=InnoDB;
CREATE TABLE tb2 LIKE tb1;

When innodb_file_per_table is 1

You get /var/lib/mysql/mydb
You get /var/lib/mysql/mydb/tb1.frm
You get /var/lib/mysql/mydb/tb1.ibd
You get /var/lib/mysql/mydb/tb2.frm
You get /var/lib/mysql/mydb/tb2.ibd

When innodb_file_per_table is 0

You get /var/lib/mysql/mydb
You get /var/lib/mysql/mydb/tb1.frm
You get /var/lib/mysql/mydb/tb2.frm

The major difference is the fact that data and index blocks for newly created tables end up inside the system tablespace file known as ibdata1 when it is 0.
Just as a pictorial reference, please note Percona's view of InnoDB

YOUR QUESTION
Changing innodb_file_per_table to 0 does not make currently created tables just migrate into ibdata1. You have to manually move those tables into ibdata1.
This will not alleviate the too many open files issues. Why ?
Regardless of storage engine, mysqld always checks for the existence of tables by first checking for the tables .frm file. Then, the mysqld process will reference the table's intergrity based on the storage engine.
In the case of InnoDB, the data dictionary of the InnoDB table is then checked.
Two file handles are opened

One file handle for the .frm
One file handle for the .ibd when accessing the table

If you move the table and index data from the .ibd into the ibdata1 file, you get this

One file handle for the .frm
One file handle for the ibdata1 when accessing the table

All the file handles will pile up inside ibdata1 instead of separate files.
STILL WANT TO MOVE TABLE INTO ibdata1 ?
While I highly discourage this, it is possible
In the example I gave you, in order to move a table into ibdata1 after setting innodb_file_per_table to 0, just run this
USE mydb
ALTER TABLE tb1 ENGINE=InnoDB;
ALTER TABLE tb2 ENGINE=InnoDB;

This recreates the table, and migrates the data and indexes into ibdata1. If you are willing to do this 240,000 times (6000 X 40), be my guest.
WHAT CAN YOU DO FROM HERE ?
You could setup MySQL Replication and perform backups on a Slave
You do the following

STOP SLAVE;
Perform mysqldump on the Slave without --single-transaction
START SLAVE;

or

STOP SLAVE;
SET GLOBAL innodb_fast_shutdown = 0;
Shutdown mysqld
Make a physical copy of the datadir
StartUp mysqld
START SLAVE;

GIVE IT A TRY !!!