Speaking as a civil war bullet digger and dealer for over 30 years, I'm quite certain the .58-caliber Minie-ball dug by ModernMiner is neither a Willaims Cleaner nor a Gardiner Explosive minie. (Timekiller, thank you for posting the excellent photos which show the proof of that to the forum's readers.) The Willaims Cleaner base-stud has a large dimple in its center ...and the Gardiner Explosive's nozzle has a large hole going all the way through it, into the minie's interior.
ModernMiner's minie is a typical "generic" version of yankee-made .58-caliber "3-groove" minie. Diggers typically called it a 3-ringer ...but what you see on its body is grooves, not rings (which are raised, not "indented').
I can say with ceertainty that there is no exact (nor even "nearly" exact) matchup for MordernMiner's minie in any of the various reference-books on civil war bullets.
Some people here who are familiar with civil war minies might think the large stud in the cavity of ModernMiner's minie is a "teat" ...which a few varieties of civil war minies do have. But that stud is much larger than any "teat" seen in the "teat-cavity" minies.
I'm also quite certain that ModernMiner's minie did not leave the factory -- or the bulletmold -- in the form we see in his photo (having a large stud-like projection in its base-cavity). Meaning, it was modified by somebody, most probably a soldier, after its original manufacture and issuance to the troops.
I can think of a possible reason a soldier modified this minie. There are two varieties of civil war bullets which were manufactured with a similar-looking stud projecting from the bullet's base. One is a Williams Cleaner (as shown in Timekiller's photos). The other is a Dimmick ...which actually has a thick stud projecting from from the center of a conical base-cavity. Perhaps a soldier had seen one of those varieties, and just for fun, decided to add a base-stud to a generic .58-caliber 3-groove minie. So, he made a hole in the minie's cavity and forced a stud into it. (Notice that the lead stud is tilted sideways, and the stud's bottom has a flattened spot, possibly from being "tapped" into the hole the soldier made.)