I've commented on these issues elsewhere, but don't have the time to look them up right now, so I'll just do a short comment here.
The Shinko tires are VERY sensitive to being mounted correctly on the rim.
I've found several sets that folks complained about this "wobble", and what it turned out to be Each and Every time was the tire was mounted on a dirty rim.
Most folks who used places like cycle gear and such, had the most problems.
They just yank the old tire off, throw the new tire on, and are done with it.
Turns out the dirt/debris on the rims don't allow the stiff sidewall to seat correctly alot of the times, causing the wobble.
I've corrected several sets that were mounted like this, and had a wobble, buy simply removing the tire, and carefully cleaning the rim, then using the correct tire paste to remount the tire correctly.
If your watching someone air up your tire, and the bead pops three or four times per side (common on dirty rims) its telling you that the tire is fighting to seat correctly, and will wobble.
The tires should be aired up with ONE loud pop per side, once seated as such, you will find there is NO wobble with these tires.
