I'm personally of the opinion that Blackfire Torch has no place in this game due to it making many strong champions even stronger, and most balanced champions still balanced. It is a mess of an item, as I'm sure you'll have found today by spectating featured matches where even Malphites, Yoricks, and Urgots are using BFT with success.
Also, what was the point of reducing mana regen on this map? This didn't impact the top set of champions at all, but it did nerf the balanced and underpowered sets. Kha'Zix, Jayce, Diana, Darius, Maokai, Teemo, Lulu, Wukong and Jax are all still manaless champions as far as any competent player is concerned, and manatank Kassadin couldn't care less about regen. On the flipside, Viktor-level/style mages are having even more issues which the new items don't really help. Reducing the map's chalice effect only increased the distance between the OPs and the non-OPs.
Nome, we have a community here that has theorycrafted solutions and mathed out tons of options all the way since the beginning of the year. Feel free to ask us for feedback on ideas, because we have a lot of constructive discussion to give, and some of the high EU players are also here on the NA forums to centralize communication.
A simple fix would be to give the Blackfire Torch DoT AP Scaling, so you'd need around 200 ap to get the damage it does now - Example 1% per tick per 100ap. Better on ap casters, worse/useless on ad's, tanks, etc. I'd also consider lowering the max charges from 25 to around 15.