Disrupting MITM attack against 3DES by intermingling plaintext and inter-mediate ciphertext between rounds
3DES
What is described here is not 3DES (Triple DES or TDES and officially the Triple Data Encryption Algorithm (TDEA or Triple DEA)). Let us call the $E$ as DES encryption and $D$ as DES decryption. Then we can write 3DES encryption as
$$E(k_3,D(k_2,E(k_1,message)))$$ with independent keys $k_1,k_2,k_3$.
The provided security by 3DES with 3 key is not 192-bits. It is around 122-bit. Therefore the 2 key variant is preferable and it is called 2TDEA.
$$E(k_1,D(k_2,E(k_1,message)))$$ in 2TDEA $k_1 = k_3$ and $k_1$ and $k_2$ are independent.
To apply the Meet-In-The-Middle (MTIM*) attack one needs cascaded ciphers. So that one can divide the encryption/decryption calls and approach from left and right build a table and find the keys with a couple of known-plaintexts.
Your Design
Your design uses the internals of the DES in a way that you defined a new cipher that has a 192-bit block size with 168-bit keys size. There is no cascading there, therefore, MITM attack is not possible.

Is it secure ( i.e. does really provide 168-bit security), we don't know. It is a new design and needs a new analysis.

*The MITM here, should not be confuse with Man-in-the-Middle attack. The later attack is an active eavesdropping