It’s established that you need to mean the Unforgivable Curses in order to use them to full potential. In the 4th book, FakeMoody tells the class that all the students there could point their wands at him and say “Avada Kedavra,” and he wouldn’t get so much as a nosebleed. Similarly, Crucio doesn’t work on Bellatrix when Harry tries it.
At the end of the 6th book, Snape kills Dumbledore with the Killing Curse. Snape says “Avada Kedavra” and hits Dumbledore with the curse, causing him to fall backwards off the tower. Afterwards, Snape and the other Death Eaters flee quickly as the Order is active and fighting their way up.
It was probably difficult for Snape to compartmentalize his feelings enough to correctly use the Killing Curse on Dumbledore. Why didn’t Snape mean it less so Dumbledore would be injured (à la nosebleed) but still alive?
My proposal: Dumbledore could have still fallen off the tower (maybe with some magic like arresto momentum so he didn’t hit the ground*), as the Death Eaters don’t check if he died. The Death Eaters (and Voldemort) would believe Dumbledore was dead. Even if the Death Eaters wanted to take a peek at the corpse, Dumbledore could just act dead.
Then, maybe Fawkes could have come and magicked his body away so no one would know. Everyone would think he was dead, but he would still secretly be alive and fighting the good fight against old Voldy.
I know his life was shortened because of the curse from the ring, but why shorten his life like that unnecessarily when he could have kept living at least a little longer?
*I know Dumbledore didn’t have his wand on him then, as Malfoy disarmed him, but he was prepared to die when this went down. If he had plans to only secretly die, he could have planned ahead of time, prepping for a fall from the tower.