Just so we don't get a duplication of answers, Karrie and I touched base (via email) on the following:
Karrie:
The 16th Engineers only served in Italy right up to the end of the war in May 0f 1945. It may be your grandfather was transferred to their unit here in the states, and then discharged.
But it's sounding like he did he stint with the 106th Infantry Div, 424th Infantry Regiment, since they began their service in the ETO in the fall of 44, which would correspond with his discharge papers. This would also fit in with the stories he related during the Battle of the Bulge.
Have you tried contacting the man listed here:
http://www.military-network.com/ben/Associations_Detail.cfm?ID=2732
If he is still alive, he may have the company rolls.
I would suggest getting in touch with NARA in Maryland (not St Louis), and finding out what records they have for the 106th Inf Div, 424th Inf Reg. This is where I obtained my dad's unit's records. This includes daily, weekly and monthly army records.
I have some other suggestions too, but this may get you started in the right direction.
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"