Applying for postdocs / lectureships - sorting bad advice from good (UK, mathematics) Long story short: I got my PhD a few years ago, and am currently in a temporary job. Anticipating future job applications, I found myself an experienced, senior local mentor. My time in this job is now almost at an end, and I've been submitting dozens of job applications, including to jobs far "below" the one I'm in now. These applications have so far all ended in rejection without interview. So I quietly reached out to some other experienced members of the faculty for their advice.

What I'm experiencing now is a case of too many mentors spoiling the broth. I have been told variously that, in order to get a job, my main, most urgent priority should be:


writing higher-quality papers to publish in top journals
polishing and publishing my older preprints, even if they're not so high-quality
speaking at conferences/seminars on the wider international stage
organising conferences / similar community admin
applying for more grants


etc. etc. I've also been given a list as long as my arm of things that are not my most urgent priority, but are still important. They're all great pieces of advice individually, but I'm finding the lack of coherent prioritisation overwhelming given the few months I have remaining, and I'm struggling to imagine how I could achieve some of these things even if I had a year or more left.


How should I be prioritising my time in the remaining few months? (For the purpose of this question, my goal is to end up not being forced out of UK academia without another job lined up.)
How should I prioritise my time in my next temporary job, if I manage to find one? (For this question, my goal is to end up with a permanent research/teaching contract in the UK within the next few years.)




Edited to add extra background information on request:


I'm in pure mathematics.
I've written several papers that have been published in good-to-very-good, well-known journals, though nothing nearing e.g. Inventiones. The preprints that I haven't yet submitted are likely to be similar. Of course, I'm working on more and better, but I am worried that I'll be forced out of academia long before any of it is finalised, much less published.
I have spoken at conferences and seminars internationally, a couple of times. I'm on the lookout for more opportunities.
I have never organised a conference or done any big admin work like that: my living situation is far too precarious to allow it, because of the lack of stable job.
The amount of smaller admin work (e.g. peer review, session chair) I've done is very limited. I'm on the lookout for opportunities, but not finding anything.
I've applied for a couple of small awards, and I'm in the process of applying for my first grant. Most of them I'm not eligible for, because they don't replace your salary, and need to be co-signed by an employer willing to pay your salary (which I don't have).
I'm aware that postdocs and fixed-term lectureships are different jobs. I include them because their job descriptions are almost identical and because I am applying for both. If you can only answer on one, or have to answer separately for each, please do.
My advice would be:


write more applications


Academic job hunt is a gamble. Boosting your CV does improve your chances, but it is still a gamble. There is no security in this game and no guaranteed strategies. Places which seem to be a 100% match can reject you without an interview, and places where you barely meet the role specification can shortlist you. There are often more criteria than are written in the job specification and there are often several competing agendas each Department wants to fulfil. 

A few months is not enough to publish your  best piece (review process may take years). Speaking at conferences may help, but realistically even if a professor will love your work and would like to hire you, they may not be able to do it immediately, unless they have funds to spare (very rare and unlikely situation in the UK). Organising a conference takes more than a year. 

tl;dr:  polish your CV and application pack, submit more job applications and (if you have time) prepare a Fellowship application, e.g. to EPSRC