The condition you are describing is the same every 03-08 KX 125&250 owners have, the fork rake is too steep, and the dogbone link is too short, the only real fix is to get the 3mm longer link,or raked out clamps, but no one makes the clamps and they don't fix the issue of the quick rising rate of the shock from the short dogbone, and Pro Circuit is out of the dogbone, with no plans to manufacture more.
Installing a steering dampner will only mask the issue not make it better, the shock will still buck and make the fork feel harsh, and the rake will still be too steep causing the twitchy feel.
Drop the forks as far down as they will go in the clamps (fork tube top flush at the cap/tube top gap) , set your race sag at 120mm. use a lot of rebound dampening (4-8 out from full clockwise) to keep the rear end low/slower rise.
Also depending on your weight, take out some compression from both the fork and shock. I was running 18 out on both w/ stock valving & springs on my 250,( same suspension, you have softer springs.
Revalve the suspension, get the proper spring rates for your weight,
If it's still twitches then get the steering dampner. I run one, but it is to fight deflection from off camber roots, not mask the issues I had with the geometry.