I’m not overly concerned about the bullet supply. Some of the resources seem to be drying up for lead and there has been a big squeeze on lead for probably 45 years. You can use lead from all the sources you mentioned. It has various amounts of antimony (tin) so the hardness varies. Plus when it is melted the dirt and some alloy will float to the top and should be dipped off. No moisture can be present of it will act like an explosive in your face.
Hardness is important if you want to drive your projectile at higher velocities. Pure lead is soft and strips out in the barrel readily over 700 fps The accumulation metal (lead or copper) in the barrel destroys accuracy.
After shtf I think solid copper bullets will be popular. Should be lots of copper and will be available from a wide variety of sources. Cast the bullets then swage them to proper dimensions.