Asking a commitee to replace a letter of recommendation? 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...
You can ask. They can say yes or no. But it might be an even better option to ask them if they will accept an additional letter that arrived too late to include. This respects everyone. 

If the answer is still no, then the professor who wrote the "replacement" letter might be convinced to send it directly to the hiring committee on his own initiative. It might be harder for them to reject it if he has a well established position that is known to them.