This has been a question that doesn’t seem to go away!
I have formed my opinion and other collectors don’t disagree but at the same time are reluctant to take a stand one way or the other.
I believe that the M&M476 / T&T 144.5 are a Selma Arsenal bullet, M&M 418 / 419 cast without a cavity plug.
The odd cylindrical extension of its base is the configuration of the gang mold opening that received the cavity plug component.
I believe that there was an alignment cone dimple sticking up for registering the location of the cavity plug assembly.
When these nose cast bullets were poured the cone dimple channelled the existing air into the cylindrical cavity hole that is present in all the recovered specimens.
If you measure the depth of individual bullets you will find that no two are the same, the dimpled mold area caused the “air pockets” to be generally the same diameter among the bullets.
I have noted that there seems to be no recovered fired specimens of this pattern suggesting that the cartridge wrappers didn’t weed out the improperly cast bullets at the time and the soldier discarded them when unread for loading fearing a jammed bullet?
As far as the rifle I believe these cartridges were made generally for the 54 caliber 1845 Mississippi Rifle.
During the Mexican war the cartridge for the rifle was a round ball, later superseded by the improved conical ball design, i.e. the 418 / 419 patterns made in Selma. These pattern were early war nose cast productions later discontinued when replaced by more efficient machine forming equipment producing the M&M 350 pattern as we know it today.
Note the earlier nose cast bullet were produced predominately in 54 caliber only and the improved machine formed continued the 54 caliber with the addition of what became the Confederate standard of .577 caliber.
Unfortunately no surviving molds are known to exist at this time to prove this speculation out but there are those who are actively looking for such artifacts or documentation.