Bouncing is usually worn-out shocks.I would locate a scale and weight both axles, 4-corner weights would be ideal. That tells if your truck loaded weight is balanced or the front axle is way underweight.
No, not IMO. an external check valve cannot compensate for the internal check valve in the pump head. I would do as stated, return it to the mfgr. for replacement. In the meantime buy a new one from Amazon and try it, their liberal return policy ...
