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We present 226 large ultra-diffuse galaxy (UDG) candidates ($r_e >5.3$\arcsec, $\mu_{0,g} > 24$ mag arcsec$^{-2}$) in the SDSS Stripe 82 regionrecovered using our improved procedure developed in anticipation of processingthe entire Legacy Surveys footprint. The advancements include less constrainedstructural parameter fitting, expanded wavelet filtering criteria,consideration of Galactic dust, estimates of parameter uncertainties andcompleteness based on simulated sources, and refinements of our automatedcandidate classification. We have a sensitivity $\sim$1 mag fainter in$\mu_{0,g}$ than the largest published catalog of this region. Using ourcompleteness-corrected sample, we find that (1) there is no significant declinein the number of UDG candidates as a function of $\mu_{0,g}$ to the limit ofour survey ($\sim$ 26.5 mag arcsec$^{-2}$); (2) bluer candidates have smallerS\'ersic $n$; (3) most blue ($g-r < 0.45$ mag) candidates have $\mu_{0,g}\lesssim 25$ mag arcsec$^{-2}$ and will fade to populate the UDG red sequencewe observe to $\sim 26.5$ mag arcsec$^{-2}$; (4) any red UDGs that existsignificantly below our $\mu_{0,g}$ sensitivity limit are not descended fromblue UDGs in our sample; and (5) candidates with lower $\mu_{0,g}$ tend tosmaller $n$. We anticipate that the final SMUDGes sample will contain $\sim$30$\times$ as many candidates.

Systematically Measuring Ultra-Diffuse Galaxies (SMUDGes). II. Expanded Survey Description and the Stripe 82 Catalog