I dug out an old 30 pin to USB cable (pre iPhone era one), a 30 pin to lightning adapter, a 12W iPad charger and a Kill-a-watt. Plugging this all into an iPad Air 2 revealed a 12W charging rate, so exactly the expected 2.4A 5V charging rate. Tried the same with an iPhone 6s and did see it go up to 6.2W on the same setup.

I'm guessing it's not going to the full 12W rate due to the battery not being below 80% like the iPad was. It's at least validation that you should be able to get it to work at more then the 2.5W level you are currently seeing. Letting the iPhone drain a bit and I'll check again later to see if it ramps up to the full fast charge rate.