We use the wealth of deep archival optical spectroscopy on the GOODS-South field to select candidate high-redshift Lyman continuum (LyC) emitters in the Hubble Deep UV Legacy Survey dataset. We find four sources with redshifts between 2.35 and 3.05 that remain detected at > 3sigma in WFC3/F275W, as well as a 2.6sigma F275W source selected by its relatively blue rest-frame UV colors. At these redshifts, the F275W filter probes only the redshifted LyC, meaning these sources are possible leakers of ionizing photons at high redshift. However, two show emission lines from intermediate-z galaxies along with lines from the high-z source, indicating contamination from line-of-sight blends. We also perform a stacking analysis on all 2.35 < z < 3.05 sources with F275W coverage in the GOODS-S and GOODS-N and find that, despite the contributions from individual candidate emitters, the typical F275W flux of this sample is extremely faint. The combined LyC emissivity of our candidates falls well below the ionizing output of AGN at similar redshifts, accounting for, at most, 14% of the metagalactic ionizing background inferred at z ~ 2.5. Finally, we note that the spectroscopic properties of our candidates show a remarkable variety, with at least two showing weak or no Lyman-a in emission. This illustrates the need to continue searching for and characterizing the lower-redshift analogs to the sources that drove reionization at z > 6, which are expected to be detected en masse by NGRST.