We present a new metric that uses the spectral curvature (SC) above 10 keV to identify Compton-thick AGN in low-quality Swift BAT X-ray data. Using NuSTAR, we observe nine high SC-selected AGN. We find that high-sensitivity spectra show the majority are Compton-thick (78% or 7/9) and the remaining two are nearly Compton-thick (NH~5-8x10^23 cm^-2). We find the SC_bat and SC_nustar measurements are consistent, suggesting this technique can be applied to future telescopes. We tested the SC method on well-known Compton-thick AGN and find it is much more effective than broad band ratios (e.g. 100% using SC vs. 20% using 8-24/3-8 keV). Our results suggest that using the >10 keV emission may be the only way to identify this population since only two sources show Compton-thick levels of excess in the OIII to X-ray emission ratio (F_OIII/F_2-10 keV>1) and WISE colors do not identify most of them as AGN. Based on this small sample, we find that a higher fraction of these AGN are in the final merger stage than typical BAT AGN. Additionally, these nine obscured AGN have, on average, four times higher accretion rates than other BAT-detected AGN (Edd ratio=0.068 compared to 0.016). The robustness of SC at identifying Compton-thick AGN implies a higher fraction of nearby AGN may be Compton-thick (~22%) and the sum of black hole growth in Compton-thick AGN (Eddington ratio times population percentage), is nearly as large as mildly obscured and unobscured AGN.