I'm with jpsdad here.. Leave cats and HBG out unless you specifically want them. Nothing there will help your goal of decent LMB.
10-15lbs of FHM will be plenty.
375 on BG doesn't sound too bad to me, maybe 75-100 RES.
As for LMB, be careful with larger fish and chose the largest for the time of year as you don't want fish that aren't growing at max rate. You have better growing conditions at your end of the state-longer as well, but If stocking larger LMB in spring I'd look for 7-8" minimum, 8-11" would be expected with the growing season you have in your area with well-fed fish from hatchery.
If someone tries to push 4-6" yr 1 LMB on you, move on.. and, if you're having trouble sourcing fish let me know, I'll set you up with 2 of Kansas's best.