This likely varies by district, of course, but in ours (CA-12 at time of nomination; reconfigured to CA-14) the nominating sources work together since there are so many competitors. They want to maximize the slate from each nominating source and not let nominations "go to waste". That was our experience, anyway. My son had an LOA, so he was told he might get the last slot, but not to worry. Her panel wanted to use the primary on someone who needed it more. We also had Boxer on standby (if that makes any sense), in case something worked out that way. It turned out it wasn't needed, and thus her nomination wasn't a duplicate. I think they really are trying to maximize the number of nominations possible.
Also, my memory is a little fuzzy, but for Feinstein you can only select one service. Boxer makes you rank them in priority (unless it is the other way around). Our congresswoman's liaison told my son that he could list choices, but would only be considered for his first, and if he selecting more than one, he better be prepared to explain himself.
They don't read any applications until the deadline - we were told that point blank. They do accept supplemental data up until the deadline. He turned in a second ACT score, additional volunteer activity, and one more EC he did.
We found all three offices to be extremely cooperative. I was always the courier since I could cut out from work, while his football coach was not as understanding.