I checked the tail over a few times since the last time I flew it, and all gears were good. I am paranoid about those gears lol. But yes, a bad gear can cause issues.
What is your gyro gain set to? Did you reset the ail and ele gains back to 50%?
You do not use any sub trim on the tail, it's all done through setup in the gyro (Not DIR mode)
To me, that looks like a wag and not a shake. The gyro is over compensating, you need to reduce your gyro gain to get rid of this. On the DX6i, 0-50% is rate mode, and 50-100% is HH mode. Set your gyro to 65% and try it (after you put new gears on the tail). If the wag is still there, reduce the gain by 2% and try again. Don't use any trim on the tail or sub trim, everything should be a factory default. Let us know how it goes when you get new tail gears on.
Also, when lifting off the ground, don't give it any cyclic input until it leaves the ground. This requires a quick takeoff and then catching the heli with right cyclic.