That's an interesting point about Col. Hawthorn having served east of the river. And to add to that, Lt. Col. Cadwallader Polk had served in the 1st Tennessee Infantry which was in Polk's Division. It certainly becomes very plausible that they would have had such a flag made for the use of their regiment.
I agree with you that there simply isn't enough evidence to determine with complete certainty which regiments the captured flags came from. Hopefully someday some previously unknown letter, diary, or recollection written by a member of these regiments will emerge and shed light on this.