Need help piecing my Grandpa's WWII story - 39th Combat Engr

[theron]

Have you tried the 39th's unit records in The National Archives (NARA)?  You can contact them by email and ask what records they hold for the regiment.  These records might include After Action reports, S-3 Message logs etc.The honors for the regiment includes the Italian landings you note.  

Since the 2nd BN did not become the 643rd until after the war was over, it suggests that your grandfather was transferred to the 643rd just to go home (having had enough points to get out).