Dear Andy,
Thanks for the question and the compliment!
First, the yips are probably due to overuse of the hands for precise control of the putter movement in putting. In the brains of people who chronically use the same repetitive fine motor control movements (violinists, calligraphers, pianists, flutists, putters...), after about two or three decades the nerve circuitry in the brain can get a little worn like a tire tread. This makes the movement feel uncertain, as if you don't quite know where the hands are located or will move to when you commit to make the downstroke.
There are other causes of the yips, but in general if the yips just sort of come on you around age 45 after playing golf since your teens, this is the first guess. The problem can be aggravated or setoff by pressure situations or even trying hard to make a putt, but fundamentally it's mostly about a certain patch in the cortex of the brain for hand movement.
Most of the stuff golfers try to get rid of the yips doesn't really address the problem effectively. In my approach, what is called for is a physical movement that doesn't involve the hands at all and therefore by-passes the worn patch. This doesn't work immediately because you have to train in the new way and also train out the old way, which is not really easy. If you want to try this, here's how:
1. Use a shoulder stroke powered by the lower back and hips turning the upper torso as a unit so the shoulderframe moves both shoulder sockets in coordination. I think of rocking a coathanger as it hangs on the rod as a pivot (in your neck-clavicle area).
2. Keep both arms nicely extended at all times by hanging them straight down naturally but all the way. I think of hanging you arms and hands by the shoulders until dead!
3.. Set and keep one level of grip pressure and don't allow it to change at any time from the beginning of the stroke until the end. This eliminates use of fine-motor muscles in the hand and forearm.
4. Start the stroke back by pushing the left shoulder back and down, thus moving your "triangle" of arms, hands, putter as a unit that keeps its shape at all times and that keeps the butt of the handle pointed at your pivot in the clavicle at all times.
5. For starters, just go back any comfortable little distance (it doesn't matter) with an easy slow tempo and let the putter head then coast to a natural state of rest at the top of the backstroke. For starters, try something like 10 inches back, or just past your rear foot, until you feel that in order to go further back you will have to start lifting the putterhead a bit. Let that be the backstroke.
6. From the resting putter position at the top of the backstroke, let your abdominal muscles give way or relax so that the heaviness of your arms and the putter just start to drop by gravity like a child on a swing coming down under the pivot of your neck.
7. Make a conscious effort NOT to hit at the ball but instead to ALLOW the putterhead to make a stable swing through the bottom of the arc, with the ball just getting in the way. Do NOT care how far it goes. Just try to keep the downswing easy and straight through the impact area. It has to bottom out before contacting the ball, so you probably want to make sure the ball is forward a bit in the stance ahead of the middle or bottom of your stroke (directly beneath your neck). Thus, play the ball opposite your heart (right handers) and just inside your left heel about two good inches ahead of the bottom of your stroke.
8. Do not make any effort to add to or detract from the swinging of the putter in the follow-through area - just let it do whatever happens as a result of falling through. However, eventually you will want to add just a slight upward movement vertically in the left shoulder so the shoulderframe as a whole returns to about where it started from. Otherwise, the relaxing of the abdominal muscles simply lets the shoulderframe drop back so the right shoulder comes down some but then at level the shoulderframe quits or resists further rocking and the arms flap underneath. To keep the triangle intact, you will need to add just a wee uptick just after impact.
You should be able to repeat this stroke as many times as you want and all balls should go the same distance on any given green. If the balls don't go almost exactly the same distance, then you still have some "hit" in your stroke, which is a hands move. Once you get rid of hit with this sort of stroke, distance control for different length putts is just an automatic matter of targeting. We can work on that later. Give this a few months. (The above is basically a combination of my tips on the Core Putt, a Straight Stroke, Tempo, and Grip Pressure, if you want to read them:
http://puttingzone.com/ziptips1.html)
With respect to the long putter, it CAN address the problem, but again only if your use of it is bypassing the bald patch in the cortex with a no-hands movement. The long putter can also be used with a hands movement. So avoid that. You really don't need a long putter, though, since a regular putter can be used with a shoulder (no hands) stroke very very well.
With respect to the left-hand dominance: hand dominance is hard to change, but in a no-hands stroke it really doesn't matter. What matters more is which side of your whole body automatically orients to a target. Are you right-eye or left-eye dominant? Check with a gunsight positioning of your two thumbs at arms length, sighting a tree or light switch off a bit with both eyes open. Close one eye. If the target remains in the sight, the open eye is your dominant eye. In general, that whole side of your body is the one that prefers to act, as in opening a door or punching out an asshole with a good cross. Forget the underhand toss - that's a hand control thing. Which side of your body would you throw a punch with? That's probably the side you want in the back side of your setup away from the hole. You want the dominant-side shoulder coming down in the downstroke.
The problem is a little complicated, however, since you are now trained to putt right-sided. I would suggest first trying to groove a stable free-fall no-hands shoulderstroke right handed with a regular putter and then experiment with reversing the symmetry of your stroke and putting mirror-like with the left, and see how that feels. I personally use centershafted putters like a bullseye or Augusta or putt-putt or Matzie that can be used either right handed or left handed. To test my faith in my stroke, I sometimes putt left handed to make sure I know how to target and make a straight stroke left handed. Believe me, I'm totally right-side dominant (except I kick left footed) and putting left handed is very unnatural for me. But a straight stroke is a straight stroke regardless of whether it is made right handed or left handed.
So, to answer your very narrow question about whether to buy a left handed long putter, I would say hold off on the long putter altogether for a bit, but if you buy one, just buy a right handed one unless you convince yourself first that you really are left-side dominant.
I hope this helps as a start, and look forward to hearing back.
Cheers!
Geoff Mangum
The PuttingZone
http://puttingzone.com
The Future of Putting Now.