Much as it pains me to concede, P2 is no longer the special wall it used to be. Chandelure beats it with specs if it uses flame body as it's ability, and is a major liability against the SubCM set (yes, such a set exists even if it isn't one of the great choice sets), or for that matter, any SubCM set, or other sub sets (damn you kingdra).
The attacking set is probably the better one now, though trace itself has merit on the set, especially against balance/stall (copying natural cure/regenerator/magic bounce is a godsend, especially the last one due to the irritation of xatu and its status inflictions). I've fought one or two analytic P2 and those are a real pain, as while not quite as powerful as the download boost, the coverage P2 gets means most slower pokemon aren't going to be wanting to stay in on P2 anyway.
Also, to add to Cims post, P2 does not appreciate togekiss's flinchhax at all, much less paraflinch. Zapdos is superior in taking that sort of strategy, especially nasty plot due to resisting air/fighting coverage that togekiss employs.
As for the fighting weakness, while fighting pokemon will beat P2 down, the only safe fighting switch I'd be backing would be shed skin scrafty, or maybe guts heracross (who won't appreciate freeze/paralysis though). The risk of status from tri-attack, or parahax from discharge if you persist with defensive sets, is far too much of a liability for any other fighting type to risk, let alone taking such hits to get in safely. Getting P2 in safely can be hard at times, but not impossible, and once in, becomes very annoying to remove.
Another thing to perhaps consider: If you're having 4MSS for P2, bear in mind while the super-effective coverage is poor, Normal-electric has perfect neutral coverage on all of UU except for Rhyperior, if you want to keep STAB tri-attack.