Is there any hope of redemption ...?

[Tuor of Gondolin]

As to the question of Gollum's possible redemption, there are two
interesting (if somewhat contradictory) views of this by JRRT in "Letters":

In #181 (written probably Jan. or Feb. 1956) he views Gollum's actual
behavior to have lead to his nonredemption:

Gollum was pitiable, but he ended in persistent wickedness, and the fact that this worked good was no credit to him. His marvelous courage and endurance, as great as Frodo and Sam's or greater, being devoted to evil was portentous, but not honorable. I am afraid, whatever our beliefs, we have to face the fact that there are persons who yield to temptation, reject their chances of nobility or salvation, and appear to be 'damnable'. Their 'damnability' is not measurable in the terms of the macrocosm (where it may work good). But we who are all 'in the same boat' must not usurp the Judge. The domination of the Ring was much too strong for the mean soul of Smeagol. But he would never have had to endure it if he had not become a mean sort of thief before it crossed his path.Need it ever have crossed his path? A kind of answer cd. be found in trying to imagine Gollum overcoming temptation. The story would have been quite different! By temporizing, not fixing the still not wholly corrupt Smeagol will towards good in the debate in the slag hole, he weakened himself for the final chance when dawning love of Frodo was too easily withered by the jealousy of Sam before Shelob's lair. After that he was lost.

While in Letter #246 (September 1963) he speculates on how a redeemed Gollum might have behaved at Mount Doom:

For me perhaps the most tragic moment in the Tale comes...when Sam fails to note the complete change in Gollum's tone and aspect. 'Nothing, nothing', said Gollum softly. 'Nice master!'. His repentence is blighted and all Frodo's pity is (in a sense) wasted. Shelob's lair becomes inevitable. This is of course do to the 'logic of the story'. Sam could hardly have acted differently. (He did reach the point of pity at last III 221-222) but for the good of Gollum too late. If he had, what could then have happened? The course of the entry into Mordor and the struggle to reach Mount Doom would have been different, and so would the ending. The interest would have shifted to Gollum, I think, and the battle that would have gone on between his repentence and his new love on one side and the Ring. Though the love would have been strengthened daily it could not have wrested the mastery from the Ring. I think that in some queer twisted and pitiable way Gollum would have tried (not maybe with conscious design) to satisfy both. Certainly at some point not long before the end he would have stolen the Ring or taken it by violence (as he does in the actual Tale). But 'possession' satisfied, I think he would then have sacrificed himself for Frodo's sake and have voluntarily cast himself into the fiery abyss.

One interesting change in view seems to be that in the first letter Tolkien lays primary "blame" for Gollum's nonredemption at his feet, while in the second letter Sam bears primary (inadvertent) responsibility.

[Lalwendë]

Those are very interesting quotes. It makes me wonder more about Sam and Gollum in relation to each other. Gollum is presented on the surface level as an evil creature, and Sam as inherently good; yet both are not necessarily these things. Gollum can repent, and Sam can be cruel. Yet more shades of grey in the morality of the story... This again sheds new light on the character of Frodo. He at first thinks of Gollum as evil, then he meets and comes to rely on him; Frodo cannot destroy the ring, and this might be seen as wrong, yet by taking on Gollum and trusting to him, he has done 'good'. Is this a particular type of Christian morality being displayed, in that mercy will eventually result in 'good'?Or is it some form of 'humanism' in that Frodo accepts the failings of another because he sees the common humanity (hobbitry?) in Gollum?

Of one thing I am sure, and that is that this clearly demonstrates the complexity in Tolkien's characters! A good one for arguments with critics.

[Tuor of Gondolin]

A bit more on Gollum/Sam, which I forgot to add above.

I also, on first reading LOTR, thought the saddest/most tragic moment
was Gollum's near repentence (and as an aside, why PJ and Andy Serkis
were so foolish in delighting in ROTK in portraying Gollum's change of heart
as being completely a ruse, against the accurate portrayal in TTT movie).

I actually think a really interesting version of LOTR would have been to
have Shelob kill off Frodo (sorry, Frodo fans ). This would have
led to a fascinating dynamic of Sam and Gollum from there to Mount Doom.
And, paranthetically, it would have quieted initial critics of LOTR that "all"
made it back safe (ignoring, of course, Boromir and the various kinds of
"losses" by the free peoples at the end of the tale).
Might Sam, as a longer term Ringbearer, have gained a greater appreciation
of Gollum's torment and been more inclined to forgiving and help redeeming
him? And as not so long a Ringbearer as Frodo, could he have resisted the
Ring's strength at the end? (Probably not, I think JRRT surmises somewhere
that the power of the Ring at Dol Guldur was too strong for anyone to
resist, which, if so, also helps to ease any criticism of Isildur).

[HerenIstarion]

a really interesting version of LOTR would have been to have Shelob kill off Frodo

I suppose it would not be LoTR any longer (I agree it would be interesting, but that would be quite different story)