I don't see how joining Red Cliff would benefit Miyabi. When teaming up with Liz alone, you might say he's in an equal position, even if he insists Liz is the one deserving all the praise (in his disgustingly phoney, boot-licking Japanese salaryman manner). But in practice their relationship is equal. Even in fights Miyabi's weird power has played a huge role. Liz has always been more than willing to pick simple resource gathering quests knowing it benefits Miyabi. So, even if he insists he's nothing but a support member, in reality they are equal. How would that work with the long-established A rank team of Red Cliff? Nah, forget it. They would fully enjoy Miyabi's extraordinary services, but he would truly be nothing but a support member in their group. They don't personally like him either, in particular. They only love Liz.
I really don't see Liz leaving Miyabi behind to join Red Cliff, either. She wouldn't feel equal at all in their company, whereas in Miyabi's company she often does, even if she still has her moments of inferiority complex. Who knows if she's in love with him or not, but I reckon she must like him as a very good friend and ally, if nothing else.
All that being said, Miyabi has got his unfortunate doormat mentality, so I wouldn't call him joining Red Cliff impossible.