I've never had to deal with head bearings on my GW, but I'm assuming it has a tapered roller bearing and I know from previous machines that that's exactly what you get if you tighten them too much, kind've more like an oscilation, than a wobble?
Mine has an occassional low speed wobble, but I wouldn't call it uncontrollable.
1. Take a close look a the tires. If either are badly cupped or show signs of damaged belts replace them.
2. Put her on the center stand and check for loosness in the front forks and stem and in the rear swing arm. It is hard to detect when they have wheels mounted to them so check carefully.
My guess if its is uncontrollable is bad or loose steering stem bearings.
1. Tires are probably badly cupped. (If you don't know what cupped tires feel like, don't feel bad. I didn't when this happened to me. Find someone who knows bike tires and have them check.)
2. the anti-dive on the front is probably set to the softest position (factory setting), change it to "3" on both sides.
3. Make sure that the rear end is tight. My blown wheel bearing and brake bar bushing was allowing my rear end to make the bike unstable.
4. Listen to everyone's advice here. They are all valid possibilities. Start with the easiest tests first. It can really be a process of elimination. If you know a good bike mechanic, it may be worth a few bucks to let him rule out some of the possibilities. Read my thread above. This is a major safety issue and can tak all the fun out of riding.