The demographics of the production and escape of ionizing photons from UV-faint early galaxies is a key unknown in discovering the primary drivers of reionization. With the advent of JWST it is finally possible to observe the rest-frame optical nebular emission from individual sub-L* z>3 galaxies to measure the production of ionizing photons, {chi}_ion_. Here we study a sample of 370 z~3-7 galaxies spanning -23<M_UV_<-15.5 (median M_UV_~-18) with deep multi-band HST and JWST/NIRCam photometry covering the rest-UV to optical from the GLASS and UNCOVER JWST surveys. Our sample includes 102 galaxies with Lyman-alpha emission detected in MUSE spectroscopy. We use H-alpha fluxes inferred from NIRCam photometry to estimate the production rate of ionizing photons which do not escape these galaxies {chi}_ion_(1-f_esc_). We find median log10{chi}ion(1-f_esc_)=25.33+/-0.47, with a broad intrinsic scatter 0.42dex, implying a broad range of galaxy properties and ages in our UV-faint sample. Galaxies detected with Lyman-alpha have ~0.1dex higher {chi}_ion_(1-f_esc_), which is explained by their higher H-alpha EW distribution, implying younger ages, higher sSFR and thus more O/B stars. We find significant trends of increasing {chi}_ion_(1-f_esc_) with increasing H-alpha EW, decreasing UV luminosity, and decreasing UV slope, implying the production of ionizing photons is enhanced in young, low metallicity galaxies. We find no significant evidence for sources with very high ionizing escape fraction (f_esc_>0.5) in our sample, based on their photometric properties, even amongst the Lyman-alpha selected galaxies. This work demonstrates that considering the full distribution of {chi}_ion_ across galaxy properties is important for assessing the primary drivers of reionization.