How to prevent a low duty cycle load from flickering lights
\$ I = \frac {V}{R} = \frac {120}{3.2} \approx 40 \ \text A \$ so it's no wonder that your lights flicker. 


The inductor will cause the current to ramp up slowly but will also cause it to run on after zero cross so this will present itself as a problematic load.
Option 2 could work but the capacitor has to get recharged on each mains half cycle and you would get large pulses of current for a brief while after the input voltage exceeds the capacitor voltage.




Figure 1. This image I had prepared for a half-wave rectifier question gives some idea of the problem. Large pulses of current are required to top-up the rectifier on each half-cycle so you would have twice as many pulses.

Another option is to series connect a reactive component with the mains. Your linked question says you require about 500 W into 3.2 Ω so you need \$ V = \sqrt {PR} = \sqrt {500 \times 3.2} = \sqrt {1600} = 40 \ \text V \$ across the resistor. The reactive component will have to drop \$ \sqrt {120^2 - 40^2} = 113 \ \text V\$ at \$ I = \frac {V}{R} = \frac {40}{3.2} = 12.5 \ \text A \$. 

The reactive impedance required is \$ Z = \frac {V}{I} = \frac {113}{12.5} = 9.04 \ Ω \$

At 60 Hz we get 


\$ C = \frac {1}{2 \pi f Z_C} = 300 \ \mu \text F\$ 


or 


\$ L = \frac {Z_L}{2 \pi f} = 24 \ \text {mH}\$.


Theoretically, either of these, rated at 12.5 A, 60 Hz, should work.