Fold3 has him in the Files for Index Cards(only one card for each soldier---usually for states that haven't had all the files scanned.
Under the Vermont folder, he is listed as SHONNIO and SHONNIE. This folder has his records containing 20+ cards.
Enlisted age 20 Height 5' 7 Inches
Born Ducksbury VT
Enlisted Nov 21. 1861.
Died at Baton Rouge Setp 3, 1863, in Hosp.
May-June 1862 Duty- Courier.
March-April 1863 Duty -Bugler
Sept-Oct 1863 -- Died of disease Sept 3rd.
(He was present in all the other roll calls.)
+ Letter 12 January 1863.
Pvt Luther Shonnio was give order to do Police duty and he replied "Ill be dxxxxxxx if I will do it." Location Camp Parapet, La.
(I don't see any document about a court martial)
+Death Certificate-- Died at USA General Hospital, Baton Rouge La Sept 3, 1863 from disease.
Artillery batteries did have companies. Maybe not all of them. Vermont had about 2 batteries of Light and Heavy artillery and maybe more. Now you need to find the history of this unit. You can try a search in Google Books for "Adjutant General Report Vermont". This might pull up a report published a few years after the war that details every regiment of that state. I haven't checked for Vermont.