High-redshift, luminous, dusty star-forming galaxies (DSFGs) constrain the extremity of galaxy formation theories. The most extreme are discovered through follow-up on candidates in large area surveys. Here, we present extensive 850
μ
m SCUBA-2 follow-up observations of 188 red DSFG candidates from the Herschel Multitiered Extragalactic Survey (HerMES) Large Mode Survey, covering 274 deg2. We detected 87 per cent with a signal-to-noise ratio >3 at 850
μ
m. We introduce a new method for incorporating the confusion noise in our spectral energy distribution fitting by sampling correlated flux density fluctuations from a confusion limited map. The new 850
μ
m data provide a better constraint on the photometric redshifts of the candidates, with photometric redshift errors decreasing from σz/(1 + z) ≈ 0.21 to 0.15. Comparison spectroscopic redshifts also found little bias (〈(z − zspec)/(1 + zspec)〉 = 0.08). The mean photometric redshift is found to be 3.6 with a dispersion of 0.4 and we identify 21 DSFGs with a high probability of lying at z > 4. After simulating our selection effects we find number counts are consistent with phenomenological galaxy evolution models. There is a statistically significant excess of WISE-1 and SDSS sources near our red galaxies, giving a strong indication that lensing may explain some of the apparently extreme objects. Nevertheless, our sample includes examples of galaxies with the highest star formation rates in the Universe (≫103 M⊙ yr−1)