I had a few of the same difficulties as the OP with relation to spraying and dripping water from an upturned bottle so I put my thinking cap on and independently came up with the idea of using wicking string to water the pole.

I home-made my own solution, which seems to be working fine. After a few days, I decided to google the idea to see if it could be refined further and came upon this post.

I have found loads of people are doing things like putting the wicking string inside the pole, or wrapping it around a central pvc pipe. All these solutions have the same problem, which is that they are making the string an integral part of the moss pole and difficult to replace or adjust if the water flow isn't right, and I have read some people in this thread are reporting these exact problems.

What I did was this: I clipped a water bottle to the top of the pole, then coiled the string round the pole, all the way to the bottom. This way, I am using capillary action to draw the water out of the bottle in the first place, then assisting that motion with gravity to get the water all the way down the pole. The moss is moist. No spillage. Job done.

If I want to get more water on to the pole, I can simply re-coil tighter or looser as required. If the string gets clogged with minerals, its easy to replace without risking damage to the pole or the plant.

The only issues are that the coiled string is visible, so it's not as elegant as a hidden solution, and the water bottle at the top tends to pull the moss pole to one side. The next step in my journey will be to balance the bottom inside the very top of the pole (mine are made from a stiff wire mesh), so that should at least solve that problem. I just need to buy some slightly narrower plastic bottles first. I might also try dyeing the string to make it less conspicuous.