You don't graft, or T bud, using a flower bud. You use a vegetative bud. The picture shown is of a T bud. You insert a vegetative bud if you want a tree. It has to be done when bark is slipping on the rootstock. That's usually June thru August. In long season areas May to Sept. Never had disease due to cuts. Not on the cut end or area of the bud or graft.

Good for you. Getting the MOST fireblight resistant varieties that produce very good fruit is the goal, whether Asian or European. What a real nice place. Another consideration would be rodents that climb fruit-laden pear trees and help themselves. If it was a concern there, I would prune away all side branches up to about 3-1/2 feet high from ground level so that when your trees have growing fruit that you can wrap a slit section of galvanized duct around the lower trunk and let it stand on the ground. As long as the rodents have no other "ladder" to climb above the duct to reach the branches, the fruit won't disappear due to hungry climbing rodents. So the T posts would need to go also. Larger diameter duct would allow steep-angled forks to remain as you bend the duct into an oval shape.

Good thinking. First, it would be good to clip healthy stems (pencil thick to 3/8" thick work well) with fat buds from the fruiting tree while the tree is still dormant, cut them to 8" lengths, dip the cut ends into melted candle wax from a wide, lit candle's puddle, lay them in a 1 gallon freezer bag with a moist pc. of paper towel, and put the bag in the fridge where it won't get bumped and crushed. You won't need to keep all the branches on the fruitless trees, so it would be good to prune away excess/unimpressive/less valuable branches before grafting time. Such as twigs and branches that grow downwards, or branches that are jammed too close together, all side growth on the bottom 4 feet of trunk (so a slit pc. of metal duct can encircle the lower trunk to keep out climbing rodents), etc. When choosing which branches to leave for grafting to, be on the lookout for vertical, fast-growing suckers from 3/8" to 1/2" thick for doing cleft grafts, as well as thicker suckers from maybe 5/8" to 1" for doing bark grafts. There is no need to whack off every branch that will not get grafted to, and leaving some of the leafy ungrafted branches will help the tree to keep growing while the young scions begin growing. Try to graft to suckers that are lower for convenience sake, and figure out which suckers are possible contenders to become the new central leader(s). It would be great to eventually have the new central leader(s) to be fruiting branches. One way to try to get that to happen is to graft some suckers near the center of the tree and graft them higher up than other grafts. Once the fruitless trees begin growing out new leaves after the last expected freeze, it is a good time to graft. If the weather has been very dry, it would be good to water the tree real well a week before the grafting. After a year of good growth for the grafted branches, more ungrafted branches could be pruned away. If you choose to, you can graft lots of extra suckers and later prune away those that do not grow as well. Over a few years of growth grafted suckers that are only a foot apart will crowd each other, so they can be pruned later. Try to graft branches over a wide area and spaced apart so as to take over the same tree circle over time. I would not graft horizontal branches at all. There are many youtube videos illustrating cleft and bark grafts. Although you may be content with the fruit from the other tree, it would be worthwhile learning from your local county agricultural extension agent which pear trees are recommended for your area, and then try to acquire dormant scions from those varieties also for grafting to such big trees that have room for lots of grafts. Fire blight resistance is a huge preference. Good luck on your worthwhile project.

tl, it was a foul wind that brought callery pear to our country. As for me, I celebrate a tree such as American Fringetree, growing happily here (N. America) since the receding ice of the Pleistocene Epoch. Fringetree is not bothered by fireblight. It is enchanting and by far more desirable than any callery pear could hope to be. This pic taken today in our local state park.