I have asked one of my thesis committee members for a letter of recommendation for a position I was applying to. He is a well-known and well-connected figure in my field, we have a good relationship and he has written me letters in the past which I am fairly certain were very good.
The only problem is that he is quite busy, and therefore unreliable: During my latest job search he submitted a letter two months late and forgot to submit another one.
The position I applied to was very important to me and I did not want to risk applying with a missing letter, so as the deadline approached and I still hadn't received a letter, I asked another, lesser-known colleague to write me a recommendation instead.
The deadline has now passed a couple of days ago and I just received my committee's member's letter on Interfolio today. I already submitted my application and I can not amend it anymore through the online application service.
Should I try contacting the search committee directly and ask if I can get the letter replaced?
I'm afraid it might sound disrespectful toward the colleague that nicely wrote me the last-minute letter, but on the other hand I think the new letter would go a long way in helping my application...