Dear OP, the actual itemization problems aren't for for AP tank or for resistances tank, the true problem are for health tank and AD/AS tanks
AP tanks have items with armor + AP (Zhonya, Iceborn Gauntlet), health + mana (Righteous Glory, RoA), health + AP(Liandry, Rylai, the same RoA), AP + MR (Abyssal, BoC, Athene), together with the classic armor + health, armor and MR + health. You can actually build a pretty much good AP/resistence tank with the actual itemization available
It's AD/AS tanks which doesn't have an item for them, as the only item with AD/AS and some defense is Wit's, but it gives little defense if you can't keep autoattacking and tanks are meant to absorb CC for allies, so in fights it end up being not so much useful
And that's why I think your item is way too overloaded.
There is no need to have in game an item with so much different stats, especially an item having AP and meant for AP tanks which are the one which are in a better situation right now and are the ones viable
P.S. The only one of the champs mentioned by you that can be defined AP tank is Maokai (and he was as matter of a fact actually in a pretty good state last season before the nerfs).
Shen is an health tank (and that's why he is actually in a bad spot), Singed is just a peculiar champ on his own because of his gameplay patterns being so much different than everything else in the league and because he relies on mana stacking as much as few other champs( es. Ryze, Urgot) leading him to be just not a meaningful example to use to judge the role of AP tanks into the game because he just builds different from a standard AP tank