We report on a comprehensive study of the growth of coherently strained GaAs quantum dots (QDs) on (111) surfaces via the Stranski-Krastanov (SK) self-assembly mechanism. Recent reports indicate that the long-standing challenge, whereby the SK growth mechanism could not be used to synthesize QDs on (111) surfaces, or QDs under tensile strain, has been overcome. However, a systematic study of the SK growth of (111)-oriented, tensile-strained QDs (TSQDs) as a function of molecular beam epitaxy growth parameters is still needed. Here, we explore the effects of deposition amount, substrate temperature, growth rate, and V/III flux ratio on the SK-driven self-assembly of GaAs(111)A TSQDs. We highlight aspects of TSQD SK self-assembly on (111) surfaces that appear to differ from the SK growth of traditional compressively strained QDs on (100) surfaces. The unique properties of (111) QDs and tensile-strained QDs mean that they are of interest for various research areas. The results discussed here offer a practical guide for tailoring the size, shape, density, uniformity, and photon emission wavelength and intensity of (111) TSQDs for future applications.