The best solution would be check for surviving examples in those states museums because of the great difference among the ones I have seen. I don't think they subscribed to a particular pattern. For instance, you mentioned what Virginia would have on theirs, but on page 225 of "Echoes of Glory: The Confederacy" it shows a Virginia drum with a shield shaped emblem with a Confederate battle flag on it attributed to the 13th VA. Infty. On the same page is one used by the 1st FL. Infty. which uses a Federal eagle. On page 227, it shows one of the 32nd NC Infty. which no painting but a simple pattern of tacks on it. The 1863 Confederate regulations state on page 11 - "the front of drums shall be painted with the arms of the Confederate States, on a blue field for infantry, and on a red field for the artillery. The letter of the company and the number of the regiment, under the arms, in a scroll. So much for sticking to Confederate regulations based on what I have seen. The 1861 United States regulations state the same verbatim except of course inserting United instead of Confederate States.
If no examples exist today, I would just use what that particular state had on their flags,buckles or buttons (ie: Mississippi - Eagle with shield) for the Southern states and the Eagle for Northern States.