I am back to suggest that rather than ask about ball size in a 40 caliber rifle, measure the bore diameter and the depth of the grooves. Are the grooves radiused or flat bottomed? Are the lands and grooves about the same width? What is the twist rate? There will still be load development. However it may narrow the starting choices for ball size, patch thickness, patch lubricant, and powder charge. Then when all is said and done, someone will have a different load in the same rifle that outperforms your best group. We missed the April "Pink Super Moon" to make incantations in the middle of a country crossroads with the rifle pointed at the moon at midnight.
Practice and consistency in loading do more to optimize accuracy than we realize. Load development gets us out to practice. Thinking about what we are doing as we analyze the results takes us along the path to improved consistency. Yup, Dave's 0.389" ball seems like just the ticket.