Higher sensitivity is a two-edged sort of thing; It can give a stronger signal, but also means that the module is inherently more sensitive to noise and interference. Also, if a local signal is very strong, it's possible that the receiver frontend detector could be overwhelmed and effectively desensitised to weaker signals near the same frequency. I still think that plugging in an inline attenuator, as counter-intuitive as is sounds, would be worth a try in this sort of situation.

pca