@Mojammn, it's basically the air pressure inside the tires that carries the load on them, and the OEM Kenda tires are lightly (& often poorly) constructed tires that
NEED those high air pressures you mention in order to carry the load that you & your Spyder put on them. But if you are now running 'real' car tires instead, tires that are constructed well enough to safely carry 2 or 3 times the weight of you & your Spyder, then I doubt that you
REALLY need that much air in the rear to carry the same load!! So by still running 28 psi in the rear, you are grossly over-inflating it and likely to suffer from a harsh ride, odd vibrations, accelerated wear, reduced traction (especially in the wet!), overworked suspension, increased risk of tire damage from road hazards/debris, and the list goes on!!
I have not yet found anyone who is heavy enough to warrant regularly running anything much more than 18 psi in any 'real' car tire fitted to a Spyder or Ryker. Sure, it might feel a little different &/or 'softer' than what you're used to at first, but if you've spent a while riding on over-inflated tires and getting used to
that feel, it'll probably take you a similar while to get used to riding on tires that are inflated closer to the ideal pressure for the load imposed upon them - and remember, these are 'Radial' tires, they are
meant to feel a bit 'soft' - that's how they provide so much better traction, ride, wear, etc, etc than cross-ply tires.
So as
@troop suggested, I'd also suggest that you run no more than about 17 psi in that rear Altimax, altho I wouldn't ever go lower than 14 psi.
And while that shake you've still got at 55-65 mph certainly
could be tires (have you checked for any abnormal wear, run-out, or defects in your 'no brand' front tires??) it could also be a lot of other things besides your tires - have you tried a proper wheel alignment (which generally means NOT a dealer!); checked (& maybe reduced??) the belt tension; considered installing a belt vibration dampener (or changing/removing it if you already have one fitted?); made sure all the suspension & driveline bearings & bushes are in good nick, etc, etc, etc??
Good Luck!