While unobscured and radio-quiet active galactic nuclei are regularly being found at redshifts $z > 6$ , their obscured and radio-loud counterparts remain elusive. We build upon our successful pilot study, presenting a new sample of low-frequency-selected candidate high-redshift radio galaxies (HzRGs) over a sky area 20 times larger. We have refined our selection technique, in which we select sources with curved radio spectra between 72-231 MHz from the GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey. In combination with the requirements that our GLEAM-selected HzRG candidates have compact radio morphologies and be undetected in near-infrared $K_s$ -band imaging from the Visible and Infrared Survey Telescope for Astronomy Kilo-degree Infrared Galaxy (VIKING) survey, we find 51 new candidate HzRGs over a sky area of approximately $1200 deg^2$ . Our sample also includes two sources from the pilot study: the second-most distant radio galaxy currently known, at $z=5.55$ , with another source potentially at $z ∼ 8$ . We present our refined selection technique and analyse the properties of the sample. We model the broadband radio spectra between 74 MHz and 9 GHz by supplementing the GLEAM data with both publicly available data and new observations from the Australia Telescope Compact Array at 5.5 and 9 GHz. In addition, deep $K_s$ -band imaging from the High-Acuity Widefield K-band Imager (HAWK-I) on the Very Large Telescope and from the Southern Herschel Astrophysical Terahertz Large Area Survey Regions $K_s$ -band Survey (SHARKS) is presented for five sources. We discuss the prospects of finding very distant radio galaxies in our sample, potentially within the epoch of reionisation at $z \gtrsim 6.5$.