Update:
Thanks to everyone that has posted on this thread so far. Every bit of information has been valuable to me, and I'm sure to many enthusiasts who I will appreciate a thread focused on this air layering process.
With the information I have received so far, I have made some alterations to the attempted air layers:
1. On each layer, I have added more sphagnum moss and compacted this much tighter against the branch.
I decided that there just would not be enough room for the roots to develop with the amount of moss that I had.
2. I have replaced the thick black plastic with multiple layers of cling film
I was worried about having air pockets that would cause the layer to fail. After watching a few DIY videos about air layering provided by links posted on this thread, I realized that clear plastic was the way to go - not just so I could see what was going on in there, but also because cling wrap really tightens the whole package up and puts pressure on the moss to compact, (hopefully) addressing the air pocket problem.
3. Replaced the everyday string with 'garden twine'
I found that its important to get string that is not too thin, because it will surely break when you are trying to tie everything in place, and not too thick, otherwise it just doesn't hold well on the layer and is loose even when knotted. I think the material used is also a factor in this. My 'garden twine' is just thick cotton thread. As I have gathered, if the layer is not tight enough, it will dry the moss out quickly.
4. Made incisions
I cut three small incisions on the top and bottom of each layer. Since they will be there for a while I am going to have to make sure they are moist enough, and that if it should rain, that the water will be able to escape without rotting the roots.
Here is one example of what I have done with all of the layers I have previously posted:
Crape Myrtle
I intend to leave most of these on until spring, unless by some miracle enough roots have developed before april. Since we get frosts here, the next thing I think I will need to address will be how to protect it from getting too cold.
Feedback and comments are much appreciated
James