All I can say is, Nashors is overrated. DFG AP Teemo works and if you don't believe me, find me on LoL and I'll prove it. My build does not contain Nashor's Tooth, I rush DFG as my first item. DFG, Q, Lich Bane proc auto-attack, good bye.
Your shroom spam will be weak regardless early game, even if you have the CDR, you won't have the mana and focusing on mana increasing items only nerfs you. Early game shrooms are to allow you farm without dying, shut down river and force the enemy to consider getting Oracles. Oracles does not make your shrooms useless, just means you can't drop them anywhere anymore. The buff to allow Teemo to carry up to 3 shrooms makes planting them immediately less important and you should take advantage of that.
Again, Early Game shrooms are not for killing, they are purely for map awareness and to shut down surprise ganks. Having 50 shrooms on the map at level 9 doesn't matter if you don't know how to place them and placing 50 shrooms by level 9 means you will be underfarmed or your shrooms are in dumb places. You need a max of 13 shrooms per lane to be safe there, that's it.
Try it first before you say it doesn't work. It's not just about getting DFG and AP to get it to work. It's about knowing how to play Teemo and this game in general and being clever with how you place Shrooms and how you make use of your tools.