These indeed look like .44 Colt bullets. However, the same bullet was used both in the .44 Colt CF round, and in the .44 paper cartridge for the M1860 revolver. As well as several other percussion rounds of the period. Both the percussion 1860, and the Richards Conversion were in use in 1871.
I would speculate from the condition of the bullets that they were from long disintegrated .44 linen/foil percussion cartridges, provided in 6 round packets of either wood or pasteboard.