Not necessarily a bigger role, but giants appear in at least one writing of Tolkien's from c.1967.
Tolkien was putting together a guide to translators of The Lord of the Rings, and he was explaining the origin of many of the place names to help guide whether they should be translated or left as is.
For Tarlang’s Neck (a pass in the white mountains that Aragorn and the Grey Company travel through), Tolkien had drafted out a legend involving a giant named Tarlang.
... Tarlang in local legend was the name of a giant of ‘long ago’ of one of the giants who in ‘ancient days’ had built the White Mountains as a wall to keep Men out of their land by the Sea. But Tarlang, while carrying a load of rock on his head, tripped and fell, and the other giants used him to finish the wall at that point, leaving his neck lying southward, while his head and the load made up the Sjouthern] mts of the ridge, [?called] Tarlangs, that separate the plain of Erech from [?Lamedon],
The Lord of the Rings: A Reader's Companion - Book V, Chapter 2
He then rewrote this note to be more descriptive:
... But owing to the facts that lang ‘neck’, though frequently used geographically, was also applied to the neck of men and animals, while Tarlang was a not uncommon man’s name*, there grew up a local legend to explain the name. It was said that when ‘in ancient days’ some giants were building the White Mountains as a wall to keep Men out of their land by the Sea, one of them called Tarlang tripped and fell on his face and as he was carrying a heavy load of rocks on his head he broke his neck and was killed. The other giants used his body to complete the wall at that point, but left his neck lying southward, leading to the three mountains of the spur: Dol Tarlang ‘Tarlang’s Head’, Cûl Veleg ‘Bigload’ and Cûl Bin ‘Little Load’. The break in his neck was shown by a depression in the ridge, near the junction with Tarlang’s Head, over which the road went.
The Lord of the Rings: A Reader's Companion - Book V, Chapter 2
Of course this is just a "legend", but giants being part of the mountains does seem to fit with the giants we meet in The Hobbit, and I think this is the only time Tolkien returned to this concept.