One can make a case for stocking LMB in fall or spring. Best way is to allow FHM to spawn for 2-4 months then add the LMB that will grow very fast due to all the 10's of thousands of FHM.
But If you are primarily interested in bigger BG then stock the LMB early (fall with others) so the first spawn of BG is heavily preyed upon by the small bass. This usually results in more crowded smaller bass, fewer BG and faster growing BG stockers. Thereafter, harvest LMB over 15"-16", manage for smaller numerous bass that keep BG to a minimum, fast growing, and large. It helps to get the BG eating pellets as soon as BG are big enought to eat the 1/8" dia pellets of Aquamax 5D05 aka 500.