Here is what I have on Company I of the 35th so far and this info comes from the MDAH files and other works available there.
Apparently at least a portion of the muster rolls of the company were destroyed by fire during the retreat from Corinth I (May 29, 1862). What I have shows "the company was *reorganized* on April 5th '62 by election of the present officers" and I have no clue why it would have been reorganized unless perhaps the original enlistment was for "state" troops and they were reorganized into a Confederate Regiment (the 35th). On or about the 15th of April, 62 the company had its full compliment of troops at 77. According to the records I have E.D. Coulter (spelling must be verified) was a private in Co. I and he claims the company was organized from Louisville Winston County. This record further states that he enlisted in the "Spring of 1861. Was in Ship Island Prison at close of war & paroled there Spring of 1865." I am fairly certain that the actual enlistment was Spring of 62 as that is when the rest of the regiment was organized and likely he was paroled to Vicksburg or Meridian. Mr. Coulter gave this description of events sometime after 1902 thus the years may have effected his memory concerning specifics. He goes on to say that his company (Co. I) was made a part of the 35th at West Point MS in the spring of 1861 (again I am sure this was meant to be 1862). Further he states that the number enlisted (rank and file) originally was 111 and unknown by him in April of 1865. Mr. Coulter was last known (by me) to be residing in Hamburg, Ashley County AR.
i am sure this is no answer to your question but I am in hopes it is a help. It pains my soul to know that there is so much out there I have as yet to learn about these glorious warriors.
Oh yes, the company's name was (from Grady Howell's "For Dixie Land I'll Take My Stand! A Muster Listing of All Known Mississippi Confederate Soldiers...) Captain Watson's Company organized from Lowndes County.
If I can be of more help or if you have any other information concerning the 35th I would love to hear from you!! I will be going back over to the MDAH at Jackson this week to do more research. Please email me at firstname.lastname@example.org or email@example.com and I will get you scans of what I have for your records.
Your humble servant,