A lengthened turned e, /ə:/, has been used for this sound in the past, and there have been disputes about the relative locations of /ɜ/ and /ə/ in the vowel chart.
Pullum and Ladusaw, Phonetic Symbol Guide, Chicago, 1996.
"Compression reduces two syllables to one, producing a long schwa which makes the word sound identical to myrrh [mɜː]."
John Wells's phonetic blog
So, the term long schwa refers to this sound, as you say, rather than to any symbolic representation of it.