I haven't got my cherry tree yet, but assuming grafting a cherry is anything like it is for apples, here are some ideas:

Do your pruning and scion collection during dormancy. I'm not sure where you are, but here in the northern hemisphere (I am in Wisconsin), right about now in March is a good time for collecting scion wood. Bag it and put it into the refrigerator until later.

Best time for grafting is when the trees just start to leaf out. An experienced friend of mine says the best time is when you see the first dandelion bloom, then you know it's time. My guess is mid-April, but with this odd weather, who knows. You basically want to make sure the sap is running in the tree before you graft on.

I'd consider chopping the tops off your trees, and throwing most of the extra wood away, but save some scions from each, make the trade and then graft up top near or on the central leader. Basically trade the tops of the two trees -- I mean, why not?! Then your new scions in the tops of the trees will get maximum sunlight which should help ensure success, assuming they don't dry out. You might want to graft two or three sticks onto each tree just to ensure success, because occasionally they die. Any graft technique should work -- saddle, whip & tongue, cleft, bench -- whatever you prefer, and based on the size of the wood you're grafting together.

Best of luck to you.

I was thinking about cleft grafting around the sides of the trunk in order to get them to be fuller and bushier. Cut a wedge in the side of the trunk at an angle, cut the scion to a wedge point, smoosh 'em together, tie 'em down and smear on the wound putty, and hope for the best.