I'm a last year PhD student in an engineering field in Europe applying for postdoc positions. I've got 2-3 months left to finish writing my dissertation and graduate. I've been working so intensely during my grad school experience that I now feel completely exhausted. Reading, writing and creative thinking is now really hard for me, even though I did well in all those three aspects during grad school. I feel my brain just shuts off at times. Over the last 1.5 year, I've written a few high-impact papers out of my PhD work and over the last few months I've been writing my dissertation. This intense writing period is a large factor why I'm also finding difficulties to write and revise text.
I've now sent out 3-4 postdoc applications, with possibly another 4-5 that I'd like to send. Every postdoc application requires that I read carefully at least a few most important papers of the prospective PI. I usually aim to read 3-5 most impactful, most cited papers very carefully, front to back (those are usually the ones where the prospective PI is either the first or the last author) and I skim 8-10 more papers (read the abstracts and conclusions, and take a quick glance at the results). Since I'm applying to postdocs that are not exactly within my PhD discipline, reading those papers requires gaining at least basic understanding of a new research area. This is really hard for me now, as I can't focus so well, I don't memorize well, and it generally takes me much longer to understand written text.
Even worse, some postdoc positions that I'm going to apply for require proposing a research idea, as it is not imposed in the postdoc offer. Those postdoc offers encourage the applicant to come up with their research idea as long as it's within the scope of the PI's research line. Over the last few months I noticed that I don't have much research creativity anymore in how to connect my skills and knowledge from my past research to what the prospective PI would like to develop. Only a few months ago I used to have that creativity. Now it's just gone. Thus, it's really hard for me even to write the 1-2 page cover letters. I look back at them, they seem poorly written, the research ideas seem shallow and I just don't know how to correct them. I used to be really good at editing my writing (based on the feedback my supervisors have been giving me in the past).
I feel like I'm at an impasse. Taking a break to rest my brain would probably help, but I don't have time to take a break. My defense date is already scheduled and I need to finish writing my dissertation. I also don't want to postpone applying for postdoc positions, as there are many positions open I'm really interested in and I'm scared of loosing those chances. What would you advise me to do? How do I apply for the postdocs efficiently? Can I for instance cut down on the amount of effort I make to get to know the research of a prospective PI and still be able to write a competitive cover letter?
Extra information: I plan on taking a >1 month break after I graduate. In my postdoc applications I indicate the starting date that takes account of that break.