Ways to help alleviate putter head wobble...
Equipment:
1. Use a heavier putter head ... ~350g
2. Use a face-balanced putter
Stroke:
1. For short putts especially, "feel" like you've locked your wrists and use primarily a shoulder-rock stroke. Or, just make sure you aren't hitting those short putts with a wristy stroke; maintain your normal back-and-through rhythm and stroke on short putts, too.
1A. Make sure you maintain a soft grip, though, so that you can feel the weight of the putter head
2. Make sure you aren't watching the putter head go back.
3. Focus on your target (or back of the cup) and program yourself to make an aggressive stroke (don't be tentative with short putts)