Our apple tree wasn't doing much of anything (it barely even ever flowered), so I finally cut it down and bark grafted 3 different varieties onto it - Liberty, Ashmead, and Cox Orange Pippin. These should all be able to pollinate one another. We also have a Honeycrisp tree nearby that should benefit from this, too.
Check out the whip and tongue graft. Very similar idea to what you described but it's much more secure and I want to say more of the cambium layer is joined together.
I took a grafting class once, and it's remarkably easy. You basically need a cutting of a similar diameter, cut diagonally.
You join the cutting to a cut twig on the tree, keeping as much of the green bark in contact as possible, and then tape it up.
You can use a salve and a special tape to improve conditions but those are the basics.
That's pretty much it!
Check out the whip and tongue graft. Very similar idea to what you described but it's much more secure and I want to say more of the cambium layer is joined together.