A well written and thoughtful essay. It is indeed a possibility that the flag has the Morris Island conenctions, and having a file on Hugh Vincent as a flag maker, he being a sail maker before the war, was used to making larger flags of the storm and garrison variety (typical of Southern flag makers who made sails before the war).
However, blockade runners also carried, like naval vessels, a full set of colors often for disguise purposes and we cannot disprove that any of the captured blockade runners in Mobile did not have this flag. We also cannot disprove it because we know that only one vessel carried a red flag - that we know of. There were hundreds of such vessels and the vast majority of their flags are missing today.
The blockade runners for the Gulf of Mexico ports ran in from Havana, Cuba typically, while those for the Eastern seabord ports ran from Nassau or Bermuda. Yet, the runners went where they were needed and as cargoes became available, so a runner in Mobile that had been in and out of Charleston is not that far-fetched.
I am not necessarily coming down on one side or the other, but a large flag like this one tends to preclude it being a unit flag especially when artillery unti flags were smaller typically than infantry flags to begin with (but not always).
It would be great if documentation from the captor states exactly where he found this flag and that would solve the problem, but dozens of CS flags were taken when Mobile fell. Most are not known, location wise, today.
But you have given a very compelling argument for the SC battery. What is the source that they moved closer to Redoubt 4?