It's certainly true that mention of the sword bayonet eliminates the better known P53 Enfield from consideration. However, the short Enfield (barrel length of two feet nine inches as opposed to three feet three inches) includes four different rifled muskets, these being the P56, P58, P58 Navy and P60. The P58 Navy used a cutlass bayonet, so we can eliminate that type. The P56 and P58 are quite similar, the main difference being the sword bar being brazed the the muzzle on the P56, the bar being on the band for the P58. Dr. C. H. Roads, The British Soldier's Firearm: From Smoothbore to Smallbore, 1850-1864, p. 94, illustrations on page 210.
It's interesting to note that the additional length of the sword bayonet made the overall length of the short Enfield virtually the same as the long Enfield. If I am not mistaken, the scabbard for the sword bayonet was made primarily of leather rather than steel.
The two service files for Deas contain a receipt showing that he was reimbursed by the Confederate government for the purchase of 400 Enfield rifles. We also have a receipt for the purchase of about eighty percussion muskets, which suggests that he didn't have enough Enfields to arm all of his companies.