A twist on OTP for an outstandingly secure channel?

Discussing about rotor machines/stream ciphers on another thread, I was
wondering what other people thought of this idea.

Imagine an OTP. Lets say 2KB of perfectly random data (key) and another
(2KB - 24 bits) of perfectly random data (used for padding). 3
character from the plaintext message are inserted where the missing 24
bits would be (assuming 8 bit characters. The missing 24 bits could be
dispersed around as randomly as the random padding data to avoid
sequential plaintext data). Now imagine that through some miracle the
attacker is able to brute force through all the keys and has all the
possible decryption at his disposal for every encrypted message
(imagine a message 15 characters long for example, this would yield 5
encrypted messages, sent across). What is the initial assumption? Full
message length, he gets nowhere.

Now imagine we give the attacker invaluable information. The
information that only 3 characters of plaintext are encrypted but he
doesn't know where. What can he do? He has to figure out what those
characters are through as many unencrypted messages as the keyspace is
large and he has to try out every combination of blocks of 3 characters
per keyspace across each keyspace per intercepted messages ranging over
a whole slew of messages (5 in our example). We have a combinatorial
explosion that is many orders of magnitudes greater than what standard,
straight up, OTP itself allows as far as protection goes. We are
magnitudes beyond being "unbreakable".

Am I missing anything?

I'm thinking that a similar scheme would be extremely useful in
compensating to the looser encryption strenght of stream ciphers. And
If the idea is sound, I would even go as far as saying that key
information exchange could be performed very safely through such a
channel.

Regards
Jean-Francois Michaud

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