[Evisse the Blue]

That was a really fascinating post, radagastly!

Two times the ring was acquired through a deliberate act of violence (Smeagol both times)
Two of them found it by some kind of chance (Deagol and Bilbo)
Twice it was given freely to the bearer (Frodo received it both times in this fashion)
and twice it was taken-on more or less 'from scratch' after the previous bearer was dead. (Isildur cut it from Sauron's dead body and Sam took it thinking Frodo was dead).

I would have included Isildur in the first category, therefore breaking the 'balance'. But I agree that Elrond's account of how the Ring came in Isildur's possesion is ambiguous and could very well prove your point:

Sauron himself was overthrown and Isildur cut the Ring from his hand(...)

This does indicate that Isildur cut the Ring after Sauron fell, but it is not clarified if Sauron was overthrown by Isildur, or by someone else, in order to be removed of the Ring.
If you're right, and Isildur falls in the same category as Sam, then this offers and interesting possibility of redemption for Isildur, if only he had released the Ring from his keeping. At one point he is ready to do that:

"It needs one greater than I know now myself to be. My pride has fallen. It should go to the Keepers of the Three."

. But it was too late, because the Ring apparently had other plans. Redemption was thus denied to him, maybe because it was not yet the time for it.

What similarity lies in the pairing of Bilbo and Sam that each of them would lay this unbearable burden onto someone they loved so dearly? This is to me one of the most obvious Christian references in the entire book.

I agree.
My thoughts on this: They seem to place the fate of many above the fate of a single individual, whom they happen to love very much. And they do it on account of their faith that everything will turn out alright, this faith which seems to many no more than 'a fool's hope'. They do it because they sense there is no other way. It appears to me that they would rather let themselves governed by the flow of events, by fate, if you will, then will things into happening. All the other Ringbearers (except Frodo) willed things into happening, and only harm came of it.