Ah, the disease of steel in full bloom. It's a terrible thing to see such a strong clean laboratory intellect being drawn into the dirty world of slag burns and hearing decay.
You have a good start on "the largish strange pieces of big iron that don't move very far or get much work done (yet)" symptom. Now maybe followed by power hammer rebuilding disorder...perhaps. You need to become good friends with John Adams, if not already. Have someone who really knows LG hammers visit and give you a cold opinion about what needs to be done.
Of the two, the bolted gibs is the newer model variation. Little Giant was known to change design features frequently. If you can find the serial number somewhere, or other features:
Indentifying your hammer
Also:
Little Giant-Mayer Bros. Power Hammer Identification Guide