I encountered the same problems during my research of my great-uncle who was killed in action serving with the 81st Infantry Division.
I also followed the same steps that Mr. Johnston has advised.The IDPF is worth its weight in gold but could take many months to get.The record center in St Louis for obtaining Army records from WWII is a waste of time.Follow through with both but do not stop digging.
To find actual accounts of what happened on 4 July 1944 you need to do couple of things. From my experience (all of the above is well worth it) but you should also do the following:
Contact the alumni assoc for the 83rd and be friendly but PERSISTENT and let them know you are a relative.Time is running out for many of our WWII vets and I would call not write the following groups and ask for a contact list of 330th Co C veterans.
83rd Infantry Div Assoc Mr. Robert Gangnath 203-266-6683 12 Hamlet Ln MonroeCT 06468-2008
83rd Boston Chapter Mr. Pat DiGiammerino Phone 781-322-2754 36 E Border Rd MaldenMA02148-1104
Buy this book (try Abebooks.com they have about 10 copies available.)It should have an account on the action on or around 4 July 1944 and might reference the action by company level and provide names.Also research the books citations list.Write down and do an internet telephone directory search on any 330th CO C soldier that received and award.LOOK for unique surnames.
Hayhow, Sgt. Ernie THE THUNDERBOLT ACROSS EUROPE A History of the 83rd Infantry Division 1942-1945 Munich N.D. Good- in Poor dust jacket. Covers worn with loss at spine head and foot. Jacket worn and torn at edges. Front hinge loose. Pages VG. ; From training to D-Day and later joining Patton's Third Army in the race across France. Photos, Fold-out color maps. Decorations, Citations, Statistics. ; 4to; 119 pages. First Edition
This all worked for me but this was over 5 years ago and time is marching on.
Let me know if you need more ideas or places to look as I have gone way overboard with this...