It doesn't sound right.

I'm sure that the load has little to do with capacitance. The resistance of a filament IS non-linear with respect to applied voltage, however.

It would appear that the measurements from your current transformer are PEAK readings, not average. Since you are using a triac - even though the lamp is on only part of the time, the peak current won't drop much at lower brightness levels. If you are using a peak detector (diode) on the output of your current transformer - or even a regular voltmeter (which actually shows .707 * Peak reading, rather than true RMS), I would expect the type of readings you are seeing.

If I was going to continue using the current transformer, I would put a load resistor across it, then feed the output to a diode into a capacitor, and then a resistor across that capacitor. My guess is that if you put a low enough value across that capacitor, you will find that it gives you a good average of the charge current, and is almost linear with respect to brightness.