You and I are thinking along the same lines most of the way here.
When I saw the initials R.A.B., I immediately figured that they were Regulus Black's initials. Who else do we know of with 2/3 confirmed initials, that would've been a deatheater and perhaps have had the opportunity to make the observations about Voldemort to realize the presence of the horcruxs. Good find on the reference to a heavy locket being at the Black residence as well. I would bet that there is probably more clues for Harry and his pals there. Otherwise, they don't seem to have much to go on beyond the memories that Dumbledore shared. Interesting that three horcruxs were actually within two seperate memories that Dumbledore had collected. The black ring, the locket and the cup. Also, the locations for where the locket and ring were both kept were also included in the memories. Who knows what other clues Dumbledore left planted in Harry through the pensieve.
I don't think Dumbledore would've countered Snape's curse either. Dumbledore was absolutely sure that his trust in Snape was well-placed and it's unlikely, after his experience with Tom Riddle, that he would misplace his trust either. Snape killing Dumbledore would probably place him very, very close to Voldemort. He couldn't have used a spell that could've been easily countered. He used "Avada Kedavra", the exact spell that Voldemort tried to use against Harry in the Ministry of Magic building.
Other things to ponder about Snape and Dumbledore's relationship. Dumbledore had consistently refused Snape to become the professor of Defense Against the Dark Arts. Why? Because Dumbledore knew that the position was cursed ever since denying Lord Voldemort the spot. Yet, Dumbledore, instead of giving the position to Slughorn, awarded Snape with the position he always wanted. Both Dumbledore AND Snape had to know that the time for both of their circumstances to change was coming. Snape got his heart's desire as a parting gesture by Dumbledore, imo. Dumbledore knew that he was probably going to die this year. That is apparent by his words to Malfoy in the end.
IMO, Dumbledore froze Harry so that he could not interfere (keeping him safe) and assured that Draco would not be the one to do it. Considering that Harry could do magic without a wand (as his numerous "accidents" with various members of the Dursley family showed in previous books), I highly doubt that Dumbledore was truly defenseless without a wand. Dumbledore put up no fight though he could clearly perform magic still. He could've easily escaped by paralyzing Draco and hopping back on the broomsticks with Harry. He merely bought time until Snape showed up. Was the "revulsion and hatred" in Snape's face present because he felt those feelings towards Dumbledore? Or was it that he hated having to do what he probably was ordered to...by Dumbledore. To protect Malfoy and Harry.
The reasoning for Harry being the final horcrux is pretty sound. It would explain some of Voldemort's traits being present in Harry. Voldemort is definitely unaware of Harry being one of his horcrux's if that is the case. He certainly wants Harry dead. This is another key about Snape that you mentioned. Snape made it clear that Harry was no match for him and yet, he didn't immobilize Harry and take him to Voldemort...Would've been a fine prize indeed but it seems obvious that Snape wants Harry alive and OUT Of Voldemort's hands. The prophecy said that "either must die at the hand of the other for neither can live while the other survives". Handing over Harry would fulfill the prophecy in Voldemort's favor. He wants Harry alive...perhaps to search out and destroy the horcruxs using the penseive memories and defeat Voldemort? That is something that neither Dumbledore or Snape can do themselves according to the prophecy. It's all up to Harry.
About Dumbledore's funeral, it was interesting that white flames appeared. Considering that Dumbledore's familiar is a phoenix....
Stephanie
In every man there is something wherein I may learn of him, and in that I am his pupil.--Ralph Waldo Emerson