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.