Hi - As to your thought the Red Palmetto Flag in the Iowa Museum is too big to have been dragged around by an artillery unit, possibly so. However, it is clear this flag was never intended to be a unit flag for Culpeper's Battery, we know this.
What connects it to the Morris Island sand battery that opened fire on the Star of the West, in addition to it being the only known example of a pure red flag with a white palmetto tree, is that the flag flying over the Morris Island battery on January 9, 1861 has been described as being a large flag.
The maker of the Morris Island flag is purported to have been Hugh Vincent. Hugh Vincent is known to have made many palmetto flags after SC secession and early in the War. He was especially known for making large flags for garrisons and also ships. There is speculation that the red palmetto flag in the museum in Iowa is a ships flag. This could also be true. But we have never found a record of a pure red palmetto flag with white palmetto for any South Carolina ships. It is unlikely that any other state's ships would be carrying a flag with a palmetto tree and a crescent which were known to be emblems of SC. Thus, we are convinced there is a connection to Morris Island.