Donna, I am a hobbyist only, not an expert. However, until you receive more informed assistance, I would offer these suggestions.
I believe the unit listed on his discharge would be the one he was in when he was mustered out of the Army. I don't believe it is necessarily the outfit wherein he spent most of his time during WWII. One possibility as to why you have not had success is, as the unit vet suggested to you, he may have been transferred into the 302nd near (or at) the end of the war.
If his personnel record at NPRC was available, it would have a transcript of the units he was in during his service. Unfortunately, from what you indicate, that record was lost in the 1973 fire.
"How can the discharge paper have more information than they are able to reconstruct?" It is because they probably have no info at all from which to reconstruct his record. What they had was lost in the fire.
There are other possible sources of info. Before making suggestions, answers to a couple of questions might be helpful.
Where did you get the, "list of men who were in Co "K" 302D Infantry during WWII who would have supposedly served with my father"?
There should be a section on the discharge, "Battles and Campaigns". What is listed there? (Some insight might be gained by comparing them with those credited to the 302nd Infantry.)
If possible, please respond and I'll see if I can help. Perhaps other (and better informed) posters will weigh in, also.