Re: 368th Engineer (General Services) Regiment

Interestingly, Bob, (if the unit is, indeed, the 368th Engineer GSR) Stanton shows a distinctive insignia for them in his Order of Battle.

Forgive my lack of heraldic expertise, but here goes with a crude description of that insignia shown in Stanton:
It is a shield (flat on top and pointed on the bottom) on which are two figures, one inside the other. The first figure resembles what a castle with six parapets might look like viewed from above. Inside that figure is what I can best describe as the four blades from a Dutch windmill, viewed face on.