Some that I did not find on your lists (maybe I am blind
)
Tenpou Ibun Ayakashi Ayashi - first epis (maybe 3 or so) are a bit odd or slow, picks up speed though. Alot of political and magical stuff.
Kousetsu Hyaku Monogatari - some horror, anti-hero a bit, but cool chars
Binbou shimai monogatari - just cute, heartwarming
The Third - speaking tank (in case the speaking bike was a turn off with Kino no Tabi), somewhat magic, female lead
Mononoke - Sequel of the last ark of Ayakashi the classic (not tenpou), if you liked that, this one is a must
Otogizoushi - has 2 arcs set in 2 times, first one is heian period, later one is modern tokyo. They are quite thrilling.
Three Kingdoms - first epis are slow, it picks up speed though, pseudo-historical
Eureka 7 - mecha
Tsukikage Ran - female samurai lead, cute second lead (chinese fighting technique), quite funny, 2000, dunno if that is already to old for you
Kemonozume - pretty gory, kinda a romeo and julia story, the woman belongs to the family who turn into monsters under certain conditions
Kaiji - gambling, very dramatic background though.
Hakkenden - magical, fighting, thrilling. Downside: some epis have such bad graphics, one can only shudder. Not many though.
Noir - a thriller. 2 female leads. I found it extremely thrilling, loved the colors and graphics in general.
Yugo the negotiator - on my list to see soon
might interest you too, when I read your lists
About the convince me list:
Kinda hard to convince you when I dont know what turned you off with a series. I definitely would suggest Basilisk, Kino no Tabi, Mushishi and more to a friend. Kino and Mushishi are very episodic, that might be a turn off. Basilisk though is one of the best ninja shows I ever saw (if one gets past the silly puppy eyes
)