OP's chips are most likely meeting spec, and they're cheap enough in volume through legitimate channels that it's not economically favorable to fake them. However, sellers on the online flea markets use keyword-spam and don't necessarily know what they're selling, and, frankly, OP's asking for quite a lot.
It's often not fully appreciated that the boost converter's switch bears the input current, not the output current. Since power is conserved across a switched-mode converter, a boost from 3.0V (low battery condition) to 12V takes in 4A (plus losses) for every 1A output. It takes a pretty low Rds(on) to pull that sort of power, and I bet the battery doesn't like it very much either.
Maybe it's easier to just put two batteries in series so as to reduce the boost ratio (and input:output current ratio).