OK so you've gotten the down and dirty lesson in Grafting, now let me expand on some stuff. Firstly if using black electrical tape, it should only be left on for one season, as it will constrict the growth of the plant.
Don't worry if not every bit of the Cambium is touching, as long as you have good contact the graft has a good chance. Different types of grafts have better percentages of success. Plant material being grafted should be from the same family i.e. Apple/Apple, Stone fruit/stone fruit.
When doing Cleft Grafts use Grafting wax to seal the grafts. Do not rely on the asphalt or tar material, or paraffin type wax. They will all crack thus making the graft no longer air tight. A cleft graft, by the way, is where you saw a limb or trunk of a tree, then make splits at the ends in order to insert the scion wood with 2-3 buds contacting what cambium you are able,.
The Bridge graft would be used where a tree or other plant is damaged, as in some animal chews the bark girdling the trunk. You can take Scion wood from the same or like plant and graft both ends of the scion across the girdled area. Don't do what I did, Please nail both ends with appropriate sized brad nails. When I used this graft I just taped it in place on both ends (I used three around the trunk of a small tree). The tree did well the first summer and well into the next spring, but then we got some big winds which broke the grafts and the tree died.
A couple of odd grafts, I have not tried but they are supposed to be compatible are, tomato grafted to the root stock of potato, or Hops Scion grafted to the root stock of the cannabis plant. (note Cannabis plants are illegal in most state without special circumstances) There are many companies selling what they refer to as fruit cocktail trees.
also there are certain grafts normally used on certain family's of trees as Bud grafting usually used for stone fruit, citrus, and small fruit trees done by the hundreds in nursery's. Splice grafts to add pollination to a tree, to add a desired variety to a small seedling or rootstock or top work small trees.
Cleft Graft is usually used to top work larger branches or tree trunks. This being said I have not heard or read any hard and fast rules regarding this. For grafting smaller (pencil sized) stock there is a tool that cuts a "keyhole" Type cut across the stock, grafts made with this tool are supposed to have a 95% success rate. Other grafts have lower success rates.
Arbor sculpture, one thing I want to try is to plant Willow whip cuttings along a line where a fence is wanted. Willows are 100% strike rate and planted at 45 degree angles opposing each other and then weave and graft to make a fence. A living growing fence might be pretty cool!!! Imagine a weeping Willow fence.