What is the purpose of letter of recommendation?
I hate that this is a legitimate question, but it is. Yes, letters are weighted heavily, in my experience. The fact that you (and many others) are often asked to write their own letters is very troubling. For one thing, it's biased. Secondly, confidentiality is absolutely violated despite most such letters being assumed as such. Now you are in the awkward position to have to write 3, and feign separate ghost writers. 

It is impossible to defend this from any logical or ethical standpoint, particularly if confidentiality is assumed. 

The best course of action is to thoughtfully ask the recommender to write his/her own letter. But you can make it easy on them by providing a CV, papers, manuscripts, etc. Give them the information you'd like to highlight but not the words.