Roger that, JW--I have 4 revolvers in 38 S&W on staff here--1 has .359" throats (Colt Police Positive), 1 has .361" throats (S&W Regulation Police), and 2 have .362+ throats and love .363" sizing (S&W M&P and a Webley-Enfield). Poetic to a fault, the 38 Short & Weak.
What I have done with the 38 S&Ws is size down .375" roundballs meant for 36 C&B revolvers to fit, then seat them deep enough so that a short bit of case mouth is above the ball radius. A dab of Lee Liquid Alox is smeared around the ball, and migrates to be held between the case mouth and ball radius. Zero leading and about 500 FPS with 1.5 grains of WW-231 moving things along.