If you can afford the NM hits from losses, and they cannot afford the manpower losses from victories, do that.
If you lose 40,000 men, they lose 20,000, but they can only replace 10,000 of those 20,000, then you will eventually win.
Grant lost every battle in the Spring of '64. But he could replace those losses, Lee couldn't replace his losses from his victories. ALSO
Naturamix wrote:there did not seem to be a way to starve it out
You're only looking at food: what about ammunition? May not be relevant in Richmond, since there are typically a number of factories there, but do they have the capacity to replace ammunition from battles?
It may be worth losing 4 battles in a row, if on the fifth attempt they can't shoot back.
I accidentally took advantage of that one time, when as the North I was attempting to break a siege of DC by attacking with multiple corps. The march to the sound of the guns didn't work for me, and I ended up making a half dozen different attacks, which obviously was not the plan. But by the last attack on day 14, the South was wore out and out of ammunition, and I broke the seige.