If this came on suddenly, after you added Extenders, i'd say look at how the wheels were reinstalled, for low pressure due to leakage from a new source, and there's always possibility a tire has failed internally. Last thing you want is a blowout.
Gently stated, you should weigh your rig and adjust tire pressure according to a Load/Pressure chart, available on sites like Michelin. Doesn't matter who made your specific tires, so long as the excat specs (Size, Profile, Load Rating) all match. Note the Chart will have pressures for Single and Dual, so read the right lines. You ARE over pressure.
Strongly stated, IF you must have Extenders, the Valves in the Rims must be METAL. Extenders on Rubber stems WILL lead to failure.
If the shimmy has been developing, then I'd include Driveshaft among my list of suspects. A loose or really stuck U-Joint'll cause commotion.