The two meds that sorted my ultradian cycling with mixed states were olanzapine ( weight side effect though) and lamotragine which was a shame because I got the dreaded rash. quitiepine stopped me in my tracks litterally I was like a zombie, not sure if this helps but really a pdoc would be better than a gp?
It's really hard to say for sure as I'm sure you probably know meds work differently for each person and you only can find out by trying them.
i never heard of advair or minoxidil, it seems meds to treat other things than psych also the others seem strange.
since you seem to suffer from other symptoms, my modest advise is to seek a hospital support, a GP is of no help here.
you went toxic on lithium, meaning you didn't monitor the dose. so either you don't have time to check or change the meds without doc consent.
suppose i tell you quetiapine helps me in my rapid cycling, would you try it. i fear you need some professional help not members here.
about rapid cycling though, bipolarity is not like people think the worst thing, it has been like this for me because i misudes antidepressants, they are the worst ennemy of BP. One doesn';t have mixed states or rapid cycling out of the blue. BP 2 "main" issues are depression and mania, and the 2nd which doctors are more worried to stop it. I almost got rid of the 2 by quetiapine/seroquel and am heading down right now using typical+atypical AP's (typical are more potent to clear the mania, but will make you more depressed). So if you don't use AD's then chance you will stabilize.
can you afford to go to a hospital