You also need authentication and integrity checking with a strong MAC which is sent with the ciphertext to prevent against bit-flipping attacks. Encrypt the MAC as well with some of the random data as well (using the same encryption process).
You'll need a way to keep in sync with the other user so you don't accidentally re-use random data. Think about how will you handle packet loss, loss of a message, or an attacker interfering. Check out the SSH protocol for some design clues. Once you've used part of the random data, it must be immediately deleted to prevent re-use. You should designate separate parts of the data for each party to send, that way both users don't accidentally send using the same random data.
Make sure your entropy is properly random. You definitely shouldn't blindly trust whatever the OS provides especially with Intel's new on-chip solution developed in collusion with the NSA and the NSA inserting backdoors into everything. Include some random user input too. You'll need a physical source of randomness probably, maybe a hardware solution and collect from multiple entropy sources. Be sure to run all entropy through a randomness extractor before you use it as well. For example, you would need to generate 128GB of entropy, then run it through Von Neumann Whitening process which will give you 64GB of usable entropy. Don't use a CSPRNG if you can help it, subtle patterns could reveal the seed used to generate the entire random data.
For 64GB that will take a while to create. If you really wanted to use a CSPRNG, potentially you could generate 3 long keys (1024 bits+). Run each through a separate CSPRNG algorithm to generate 3 separate outputs of 128GB. Then run the separate outputs through the entropy extractor giving you 64GB for each output, then finally XOR the outputs together (output1 XOR output2 XOR output3). The final output should be good for 64GB of secure random data and unpredictable for any attacker.
The beauty of the one-time pad is that the ciphertext can be decrypted to any plaintext of the same length. An attacker can try all the keys they want, it will just reveal all possible plaintexts. If you maintain proper key management (deleting keys after use) and other security around the implementation then you have plausible deniability. If an attacker forces you to reveal your key (with a rubber hose or wrench) then you no longer have the key to help them. And anything you sent could plausibly be changed to anything you want to say instead. There's a reason military and governments still use it. Once quantum cryptography key exchange becomes more widely available the one-time pad will be even more used. Until then, deal with the minor practical hassles and enjoy freedom and perfect secrecy.