JdgDReDD,I had the same issue with the Gen 2 suspension.
I found the balance of the bike was off, meaning that too much of the bikes weight was on the front end when riding solo/unloaded.
I built a .75" Lowering kit for the back suspension and that solved all my issues.
Steering bearings were good, and properly adjusted. wheel brgs, spokes, fork bushings all good.
I'm in the process of building fork caps that will allow the forks to be lowered .5-.75 " which will raise the front end that much taking the excess weight off the front end. This will work for those that can't afford to soften the back suspension(heavier riders/touring load).
Again this should solve the weight transfer issue allowing a person to run the stock rear link.
I ride solo and the marginally softer rear suspension works well for my weight, 170 lbs. and could probably accommodate a 225 lbs rider nicely.
Hope this helps. What you're feeling is the forks flexing in the bushing play, yes there is play, there has to be clearance for them to move. The fact that the bike is in a constant nose dive due to Gen 2 suspension geometry is the issue i believe. Lower the back, raise the front. Either will solve your issues.
Nay sayers will doubt this post but ... it is what it is.
here an image of my .75" lowering link.
I had a few extras made up, as it was nearly the same price to make 10 sets as it was to make 1 set. Let me know if you're interested. They are cut from 1/4" stainless with a plasma cutter. I finish the holes by hand with an air grinder. They worked out pretty nice actually and the ride is sweet.
I call it the "Commuter Ride"
Be sure to tighten the front axle pinch bolts to spec after pushing the front end down a few times to center the forks on the axle.
I am guessing you have an 08 to 14.5 Gen 2 with the softer suspension. Your bike sounds like it rides like my friends 09. My 2016 NE has very stiff springs and damping, and the bike rode in "easy rider" mode with the forks at near full extension with the front raked out and forks never getting anywhere close to bottoming off road despite the weight. I ended completely rebuilding the forks, then raising them 15mm and putting 5W in them just to get more weight on the front end and get them to move, which they now do. Now that I have the cause of the oscillation identified and just about resolved, I can now think about suspension tuning. Finally!
I'll keep the links in mind...it is quite a swing to get my 30" inseam leg over the KLR! haha!