Tolkien introduced ᴹ√EL as the basis for Elvish star-words in The Etymologies of the 1930s at the same time as he devised a new etymology for the words for “Elf” as the “Star-Folk” using an extended form of this root ᴹ√ELED (Ety/EL, ELED). The extended root √ELED seems to have survived at least up until around 1950, where it appear among list of examples of roots for Elvish tribal names, with deleted variant √EDEL (PE18/84). But later on the extend form seems to have fallen away, at least as the basis for Elf-words, being replaced in the Quendi and Eldar essay from 1959-60 by the root √DEL “walk, go, proceed, travel” and its Quenya-only variant √LED.
In the Quendi and Eldar essay, the words for “Elf” were recontextualized as a blend of the senses “star” and “departure”, referring to Elves both as the people of the stars and the specific group of the Eldar as those Elves who left for Aman (WJ/362-3). In these same notes Tolkien said that ele originated first as an interjection meaning “lo!, behold!”, as uttered when the Elves first beheld the stars (WJ/360). In this sense, it might have been a partial restoration of a (hypothetical) early root ✱ᴱ√ELE used for various words of wonderment and “otherness” in the 1910s and 20s; see that entry for details.
The root ᴹ√STAR “stiff” appeared in The Etymologies of the 1930s with derivatives like ᴹQ. sara/N. thâr “stiff grass” and N. tharn “sapless, stiff, rigid, withered” (Ety/STAR). It had an extended variant ᴹ√STARAN serving as the basis for Ilk. thrôn “stiff, hard” in Ilk. Belthronding (Ety/STARAN). The root √STAR reappeared unglossed in Common Eldarin: Verb Structure of the early 1950s as a verbal root to illustrate certain patterns in the formation of perfect tenses; as such it may not be a “real” appearance of the root (PE22/133).