Same shaft screw was loose on my HX686P, which appears to be same as HX6829 in Philips' site's troubleshooter, and the loose screw was causing the toothbrush to buzz loudly, but not vibrate the head very much. I used a #1 Phillips screwdriver to loosen but not remove the screw, then applied some blue Loctite with a toothpick to the threads, then tighten the screw, which resolved the problem.

BTW, that Phillips #1 was on my HX686P (purchased as one of a pair at Costco in the US, which seems to be the same as an HX6829 when I try to look it up on Philips' website in their troubleshooter).

I believe I used a Phillips #1 on that screw. #0 seemed too small to me.

After turning off the water supply, be sure to flush a few times to get as much water out of the tank as possible..

Then, then sponge out the rest before removing the water supply hose from the bottom of the tank.

I've heard you can use a plunger to get the remaining water that's in the toilet bowl out, or a shop vac could work, too.