While the tires could very well be junk, but this would not explain the vibration as you have described it.
This type of vibration that you have explained almost indicates some binding in the rear driveline. When was the last time that the splines in the slip joint were greased?
Taking the boot off is a piece of cake, and as you already know, this slip joint does not have a grease fitting, so it has to be taken apart to be greased.
A binding slip joint here will truly cause a problem such as this, and once it gets worse, it develops a pretty good noise, and the vibration under acceleration and deceleration will get worse.
Its worth looking at anyway.