The 300 uF capacitor, which you have marked as may not be needed, is electrically in parallel with the other big cap, 1000-2000 uF. It's use would depend on your exact physical layout. Although I would probably add a 0.1 uF in parallel with it, help mop up any rf noise generated.
I'd also use larger value pots, possibly decreasing the value of the 0.0047 uF cap. As shown, each adjustment only spans a 6:1 range. The giveaway here is your statement that in your setup, R2 = 6K works best. You're at the end of your adjustment. Maybe R2 = 8K, or 10K, might work even better?
Also be aware that the 2 pots interact.
I have to query your statement about setting R2 to 6K to start with. This just looks wrong.
And don't skimp on that flyback diode across the fet. The circuit will work without it, though the mosfet is more likely to go bye-byes.
Amanda