There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
húme
cardinal. thousand; †great number
tuksa kainen
cardinal. thousand
A variant word for “thousand” from the Early Qenya Grammar (EQG) of the 1920s as a combination of ᴱQ. tuksa “hundred” and ᴱQ. kainen “ten”, following the pattern of words like ᴱQ. kan(ta)kainen “forty” (PE14/50, 83). Properly it is tuksa kainen, shortened to either tuksakainen or tuksainen. Compare ᴱQ. húme “thousand”.
maite
cardinal. thousand
tuksainen
cardinal. thousand
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
The Early Qenya Grammar (EQG) of the 1920s had several different words for “thousand”. The manuscript version had ᴱQ. {súme >> húme >> ellume >>} húme “thousand”, originally meaning “a great number” (PE14/50 and note #56). The typescript version had ᴱQ. maite (maisi-) “thousand” (PE14/83).
Neo-Quenya: For purposes of Neo-Quenya, I use ᴺQ. húmë “thousand” since Q. maitë means “handy; handed” in Tolkien’s later writings. Some Neo-Quenya writers prefer ᴺQ. mencë “thousand” as a hypothetical cognate to S. meneg.