I recently applied for several postdoc positions. Two of them ("A" and "B") are closely related to my doctoral dissertation topic, and these applications were quite strongly welcomed. I am already in the process of negotiations regarding one of them. However, the salaries are on the low side, and I don't have an official job offer yet.
On the other hand, one of the postdoc positions ("C") I applied for is in a different field of study, but the pay is more than twice as high compared to the other two, and it would probably be considered more prestigious. The principal investigator (PI) immediately contacted me after I applied and asked me to have my references submit their reference letters.
The issue is that my main reference -- my dissertation advisor -- is sceptical about the application for position C: he says that it is likely to have a large number of competing applicants, and the interest in my application may be low or non-existent. Also, he shares the opinion that it is awkward to pursue another application when I am practically hired in my field (where everyone knows each other as well). He suggested me to wait and see if there the PI associated with position C will follow up and show more interest.
I would definitely be interested in seeing what happens with the application for position C. My question is, would it be indeed a good strategy to wait to see if the PI of position C is going to follow up, or could I perhaps ask him to continue with my application without the reference letters for now (in order to not insist that my dissertation advisor goes ahead and writes a reference letter)?