You note about the sap is flowing, I observed, it never stops! I made lot's of dormant cuts this year, and sap was all over. Sap flowing seems not to tell you much with figs. When Fruitnut was talking about the Cambium layer he mentions it is cream colored that the green is the inner layer of bark. One should be able to tell once bark is slipping. I want to try the budding figs too. His tutorial was very clear. Also using thicker scion is fine, used all the time in fruit tree grafting.
Apical dominance is the phenomenon whereby the main, central stem of the plant is dominant over (i.e., grows more strongly than) other side stems; on a branch the main stem of the branch is further dominant over its own side branchlets. This is important in knowing how to control scaffolds, and shape a tree.
See http://www.plantphys.info/apical/apical.html
I have found the fewer cuts I make, the better. It's hard to get a flat smooth surface, and the key to good take is making a flat smooth surface. The best way to make one is with one cut. I know with wedge grafts you have to make a few, as you're angling the wood. But if you can do it with the least amount of strokes, you will increase your takes. If I use more than five, I scrape the scion and start over.
I would also consider using whip grafts, wedge grafts are great when rootstocks are large and scion is small. Anything else they lose their advantage. Although easy to do compared to whip or tongue and whip grafts.
Many good videos on grafting fruit trees is out there, and a fig is just another fruit tree. I suggest people check them out.
You want to do this right. The graft is going to have to bear the weight of the fruit. If done poorly it will break on you. Unless you're doing it for other reasons. I myself will be grafting lower on the rootstock.
A good whip graft that takes, the graft itself will be hard to see as it aligns perfectly. It produces a strong union.
You may want to remove fruit the first year to let the graft bond as much as possible and also to grow in size.
Sorry to be critical just trying to get out correct info.
For fun I will be making a multiple grafted tree with 3 or 4 fig varieties, it saves room too. Having 4 varities on one tree, means I have room for more plants and more varieties.
This is a good breakdown of various grafting techniques, and loads of good info. I suggest you look at it before attempting any grafts.
https://content.ces.ncsu.edu/grafting-and-budding-nursery-crop-plants
Harvey's videos are good too!