We use the wealth of deep archival optical spectroscopy on the GOODS-South field from Keck, the VLT, and other facilities to select candidate high-redshift Lyman continuum (LyC) leakers in the Hubble Deep UV Legacy Survey (HDUV) dataset. We select sources at $2.35 < z < 3.05$, where the HST/WFC3 F275W filter probes only the redshifted LyC. We find five moderately F275W-bright sources (four detected at $gtrsim3sigma$ significance) in this redshift range. However, two of these show evidence in their optical spectra for contamination by foreground galaxies along the line-of-sight. We then perform an F275W error-weighted sum of the fluxes of all 129 galaxies at $2.35 < z < 3.05$ in both the GOODS-N and GOODS-S HDUV areas to estimate the total ionizing flux. The result is dominated by just five candidate F275W-bright LyC sources. Lastly, we examine the contributions to the metagalactic ionizing background, finding that, at the sensitivity of the HDUV F275W data and allowing for the effects of LyC transmission in the intergalactic medium (IGM), star-forming galaxies can match the UV flux required to maintain an ionized IGM at $z sim 2.5$.