By all means use whatever length stroke on the short ones that helps you get it online exactly where you aim it for read, just so you read and plan the putt with the same delivery pace that you actually execute the stroke with. That's mostly "rhythm", whereas changing the tempo will change the size of the stroke. It's ok to change the tempo and size, but try to stick to an same-same back and thru rhythm whatever tempo you use for short putts (i.e., quicker and shorter strokes).
There is a lot more to sinking short putts. Identify different ranges:
0-2 feet, (almost) never enough break to worry about (99.9% of the time) -- just aim slightly to the high side of the inside of the cup and roll it straight.
2-5 feet, until the slope and green speed combination gets to a certain severity, all of these putts are still not aiming outside the hole, but are probably fine aiming to the high-side edge of the cup. For mild to normal slopes and normal green speeds, any putts in this range are probably not outside the edge.
5-20 feet, there are rules of thumb for the break with the aim being a spot above the hole on the fall line so many inches above the top lip:
1% slope: distance/3 = inches to aim (e.g., 9' putt aim 3" high; 12' putt aim 4" high etc.)
2% slope: 2xdistance/3 = inches to aim (e.g., 9' putt, aim 2x9/3 = 6" high; 12' putt, aim 2x12/3 = 8" high etc.)
3% slope: 3xdistance/3 or simply distance in feet = inches to aim (e.g., 9' putt aim 9" high, 12' putt aim 12" high)
4% slope: 4xdistance/3 = inches to aim (e.g., 9' putt, aim 4x9/3 = 12" high; 12' putt, aim 4x12/3 = 16" high)
The above aims all assume the surface is not changing shape between ball and hole but is flat and tilted the same orientation in space (flat-but-tilted). To decide how steep the slope is, find trhe fall line, walk three paces below the hole plus about 10" more, then assess the elevation difference between your foot and the hole, with the following showing slope percents:
hole half as high as top of toe of shoe: 1%
hole as high as top of toe on shoe: 2%
hole as high as top of laces on shoe: 3%
hole as high as ankle above foot: 4%
These are "ballpark" reads that will have to be fine-tuned to your specific delivery pace and the actual green speed and contour shapes, but that is always the case.
The interesting case is the 3% slope. For the normal green speeds, this is the most common slope and these putts breaks the same number of inches as the distance of the putt in feet. A 10' putt usually breaks 10", etc. So that's a very convenient ballpark.
With these three basic ranges (0-2, 2-5, and 5-20), you can start sinking many more "short" putts.
As to the shaft lean, don't pay any attention to anyone else, especially weirdo Zach, and simply do what you think is simplest and easiest to stroke the ball dead straight wherever the putter face aims.
There is more of this on this webpage in the PuttingZone:http://puttingzone.com/vector.html
Putting Coach and Theorist