I'm not sure Tyrion's actual plan is 100% known, even to Tyrion. At the start of ADWD he was despondent and lost, a kinslayer and falsely accused kingslayer. He was foresaken, hunted and had zero chance of getting credit for his deeds or claiming Castlery Rock as his own. After he sobers up he is ostensbily placed in league with Jon Connington and "Aegon Targaryn" who may or may not be a fake, because "Aegon" was seeking Dany and Tryion could be an advisor as to the inner dealings of Westeros, in addition to having read quite a bit about dragons (to the point of obsession). From his own motiviations, Tyrion sees a chance to return to Westeros and seek vengance against his sister, his brother and anyone else he percieves to have wronged him and take what is his by rights. In this regard, he convinces Aegon to conquer Westeros and then seek Dany's approval. This is, simply stated, the "Tyrion plot" of ADWD. What is Tyrion's actual plan? We don't know. He never shares is specifically with the reader. He clearly intended to hook on with Aegon and return to Westeros until he has the misfortune of running into Jorah Mormont. Then, he hatches a plan to enlist the aid of sellswords to help Dany and eventually, in some way, get back to Westeros. How? We don't know except that when Tyrion signs up with the Second Sons he agrees to pay them upon him coming into his rightful inheritence at Castlery Rock - which he plans to either take or die in the attempt.