I have tried a variety of methods to enhance my training: working on the floor and on the parallettes, with band support in doing handstand push ups, with a spotter, doing wall handstands and most recently, working the shoulder stand.
If you saw the post on Death Metal you know what I mean. I have been working the transition from L sit to shoulder stand rather regularly (as my clients will likely tell you), and slowly but surely my comfort and ability to maintain the position for longer periods of time has increased. Most recently, I have confirmed that I can do sets of 20 seconds or more most of the time.
Of all the supplemental methods, I would rank spotting very highly, as well as wall handstands. However, it is with shoulder stands that I feel like I have gained the most in terms of time and ability to stabilize. And it feels like it's from strength.
Let me explain. When performing the shoulder stand, there is a very high level of tension in the wrist, forearm, elbow, upper arm and shoulder the entire time you are holding it. You maintain your balance by way of straightening or bending your body, mostly at the hip, and by bending your wrists. Those of you who do Judo will know what I mean. It feels like 'answering the phone' on the collar grip. For those of you who passed some sort of bio mechanics or kinesiology course, we're talking mostly about a fine balance controlled through forceful radial or ulnar deviation at the wrist. The thing is, while you hold the shoulder stand, you have to force most of your balance by pulling against your own bodyweight with those motions at the wrist on the parallettes.
As I have gained the ability to do this for longer periods of time, I have noticed it's much easier to do the same thing whilst in the handstand, and as such, to use pure grip strength essentially to make minute adjustments to balance with the wrists, and more gross adjustments with the legs.
Here's some video to show the two: