Unlikely / Impossible

Dismissing something out of hand, among friends.

～っこない vs ～そうにない: Use っこない. It is blunt spoken denial ('no way that's happening'). そうにない is a neutral assessment that something looks unlikely, so it lacks the dismissiveness and is the one to use in writing.

There is genuinely no means of doing it.

～ようがない vs ～ものか: Use ようがない: 連絡しようがない. It says no method exists, which is a statement about the world. ものか is a rhetorical refusal ('as if I would'), which is a statement about your own will.