TBH, I don't think EU could pressure Turkey into anything. Not at this point. With the US and Russia competing for Erdogan's support, the EU is no longer an important in that game. Indeed, should EU push Turkey away, Russia will be more than happy to pick up the slack. If Erdogan is anything like Stalin was, he wouldn't give much thought to foreign cries to spare the conspirators, either. Regardless of whether he wants to be closer to Russia or to US, he's not going to go easy on the opposition.
Sure, you don't want to intervene in the civil war, but considering everything, can we really say it's still a civil war? It seems like whatever opposition Erdogan had has been crushed already. Of course, there's still a matter of armed civilians in the streets. The military is still weak, though, and a foreign invasion at this point would probably be about no harder than the US invasion of Iraq, where the regular armed forces were quickly overrun. Pulling off an occupation after that could be though (and could very well turn into Iraq if botched), but if your goal wasn't to take over the whole country, but just take some of its territory, this could be workable from a purely military standpoint.
Indeed, I wonder how Kurds feature in all this. They've wanted their own state for quite a while and I don't think they're onboard with Erdogan's Islamic dictatorship. Not that they were ever big on Turkey in general. Considering how they were treated before the coup, it seems like they'd really want to kick Turks out and become independent before Erdogan starts sending them to concentration camps.