You're Correct!
For many club golfers, the thought of playing golf at a course where the greens are fast is a nightmare. Not knowing how hard to hit your putt or the feeling that you have no control how far it will travel is the biggest problem. This is mainly all down to the fact that you dont know how to control your speed.
No matter how fast or slow the greens are, the most important factor that you must control in order to be a consistent putter is the speed of your putts. For example, if you were to hit six putts making a putting stroke, with a backstroke that stopped only just outside your trailing foot, then a forward stroke that finished four inches outside your lead foot, as long as you keep the speed tempo of your stroke the same in both directions, you should see a very good and close grouping of balls. If you were to pace out the distance to the centre of this group, you will know the distance this length of stroke will hit your putts.
If you were on your local golf course and faced a fairly level putt of this length, you now have the length of stroke to control the speed of your putt for the required distance. If you were playing at a course where the speed of the greens were faster than those that you are used to, then you just need to shorten the length of your backstroke while taking care to maintain the constant tempo of your stroke in both directions.
One thing that you must take into account before you decide by how much the length of the backstroke needs to be shortened, would be to assess any slopes that may influence the roll of your putt. If the green is fast and your putt is downhill then the length of your stroke will need to be very small, yet if your putt was uphill, you would still need to make a fairly normal stroke to allow for the degree of incline.
Sorry Try Again! - See Explanation Below
By making your stroke longer and slower you will find it very difficult to consistently control the speed of your putts. Even with the added pace in the green, a putting stroke that decelerates will never be able to produce consistent results.
Sorry Try Again! - See Explanation Below
Spending money on a new putter just to try and produce a softer feel is unnecessary and still wouldnt guarantee you success on faster greens. You should invest your money into some putting lessons with a PGA professional to provide you with the right putting stroke and set up for you.
Sorry Try Again! - See Explanation Below
If you were to stop your follow through around your lead foot then your stroke will have begun to decelerate before you had made an impact with your ball. This slower speed at impact will result in you leaving your putts short of the hole almost every time.