Once the ships got Grant’s troops across the Mississippi River, they were used to shell Vicksburg until Grant had Pemberton penned up in Vicksburg. From that point on they were instrumental in keeping Grant’s forces resupplied with ammunition, provisions and fodder. In addition they kept up nearly a 24 hour bombardment of the city of Vicksburg until
the city surrendered.
So he really didn’t have that much of a problem with outrunning his logistics, did he?