And you assume this cylon won't just play one TRE card why? Considering how this system works, everyone can just play whatever the hell they want and what we'd be left with will at best be clues.
If me, Kevin, Jaybee, Wen, RD and WoMC play all our positive cards, we should be far into the positive and be left with a relatively small pool of suspects if things do go awry. And the chance of things going awry is relatively small, considering one prime suspect, Wen, has only 1 TRE card to play, and we have no reason to suspect the others just yet.
Remember that there is no sure fire way to success, so what we wanna do is narrow down our list of suspects as much as possible and not mindlessly spam all our skills because the consequence of failing the skill check looks crippling. Remember this is only month 2, we are going to be given a chance to recover.