There is little reference or attention given to supporting and attached units such as AmTrac Battalions, making specifics difficult to locate. The following is from Across the Reef by Victor J. Croizat and is the only reference to the 56th states that the Army 56th Amphibian Tank Battalion provided 18 LVT(A)s from its “A” Company to lead the two battalions of the 1st Marines embarked aboard 164 LVT3Cs of the 1st Amphibian Tractor Battalion landing on Blue Beaches at Inchon.
Good luck on your hunt, if I come across more information I will post.
WIP:
Trying to get my hobby stuff sorted - just moved and still unpacking.
"Gator, Green Catskill....Charlie On Time"