You did dig at least one civil war military bullet... it appears to be a Williams Patent "bore-cleaner" bullet. (All of those are .58-caliber.) It could be a Williams Type 1, which had a base-stud like what we see in your photo... or a Williams Type 3, which had a flat disc attached to the base-stud, with the disc broken off from your bullet. If you found it at a Siege-of-Petersburg site (1864-65), the statistical odds favor it being a Type 3.