I was wondering if using randomly generated shared 1GB or so file as a kind of one-time pad would be useful. Xor data with it using it as circular buffer, do messages must be of the same length or it will go out of sync.
If you're only reusing it once, then I guess frequency analysis gets tricky, but the problem you have instead is that you have provided a validation function: Where, using a one-time-pad, any key that yields plausible cleartext is a possible candidate, if you have two cyphertexts encoded with the same (piece of) the one-time-pad, only keys that result in plausible decrypted cleartext for both cyphertexts are possible candidates.
This was how an early break-through in breaking the Enigma was achieved (tangentially, as the Enigma isn't a one-time-pad, but the analysis is similar): Codes were rotated daily, but the first message sent out every morning with the new codes was a weather-report. Thus, the team could immediately cull the search-space to keys that would decrypt to "Weather on [date]" for the first n characters.