To check (in this particular order):
Tyre pressures. The DR should be stable at anything above 1.4 bar front. To get decent service life out of your tyres you should run 1.7 bar f & r and go up to 2 bar with the rear if you've got half the household on the back or do highway speed.
Knobblies should be run harder on tar than dual purpose tyres but that's more to make them last a bit longer.
Steering head bearings & wheel bearings.
Both will be close to perishing at your mileage. The original steering head due to lack of grease on assembly. The wheel bearings are only sealed on the outside and moisture will by now have turned the grease into margarine and caused corrosion & wear.
The DR650SE is not prone to develop high speed wobble and I would say the Wilbers springs rather make the bike more stable.
As long as the rear shock is not fitted with a spring much stiffer than OEM or the preload adjusted way over the max. allowed setup I don't think the rear suspension setup has the potential to cause the problem.
BTW high speed wobble will typically be caused by too much rear spring preload which increases (steepens) the steering head angle, reducing front wheel trail and inherent stability.
Very aggressive MX patterns do have the potential to cause high speed stability issues. If you have ruled out all other possibilities you might have to find other tyres or slow down. (Volroom is right).
Also try to stick to a combination of tyres with the same oer similar characteristics front and rear. (as in the same pattern or combos like Bridgestone TW41 / 42). Handling problems are one point, different grip on tar / dirt or especially on wet tar are another one. A wildly over- or understeering bike is neither fun nor safe to ride
