The spelling of "gyrosa" may seem confusing, but it actually follows common patterns in English. In IPA phonetic transcription, it would be written as /dʒaɪˈroʊzə/. The "gy" at the beginning is pronounced like a "j" sound, as in "jive." The "ro" is pronounced like "roe," or the eggs of fish. The "sa" ending can be spelled with either a "s" or "z" depending on the pronunciation of the preceding sound, in this case the "o" sound. So the correct spelling of "gyrosa" reflects the English pronunciation of the word.
Sham-movement vertigo.
A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.