I found two Honeycutt's in the roster of the Confederate Dead but not the one you're looking for.

Honeycutt G. M. Born:
Buried: Confederate Cemetery, Chattanoog Died:
Rank/Regt: F 11th LA Regt.
Reference: Confederate Cemetery

Honeycutt W. F. Born:
Buried: Green Lawn Cemetery, Camp Morton, IN Died:
Rank/Regt: E 30th TN
Reference: CV 1-1914, V. XXII, No. 1

Roster of Confederate Soldiers, 1861-1865 shows:

Honeycutt, L.G. AL 41st Inf. Co.G

You might want to try contacting:
State of Alabama
Department of Archives and History
624 Washington Avenue
Montgomery, AL 36130

Archival Services: 205-242-4152
Refernce Room: 205-242-4435

They have a list of casualties and deaths in hospitals.