I am not sure whether this question is suitable for academia, if not it would be great to know the site where I should ask this. I am a finishing Ph.D. student in Mathematics at a decent school in the US, and my postdoctoral job applications so far have gone in vein, although I do have published paper in recognized journal. Also, I had to switch my advisor and subject in the middle of my Ph.D., so I think I would have been better off with more experience in the field I am working on or a related field. That would mean even if I get a postdoc, I would feel a little bit inferior to other postdocs or might seek a little more help from my mentor.
I noticed the postings by some European Universities for postdocs where they mention that they are looking for postdocs and Ph.D. students both. Although I will be applying for postdocs in these universities, I was thinking of having your opinion on the following, somewhat irregular backup plan:
Say University U in Europe has a postdoc position P for salary x for 2 years, and Ph.D. position D for salary y for 4 years, where x>y. If I can get P, great, but if not, can I also talk to and try to come to an agreement with the university (e-mail them with explanation etc.) for a visiting position where I will be learning some more stuffs and will be researching as well, but may be with less salary than P but the same (or little more) salary as/than D? In other words, I feel like I need to gain more knowledge in my area, so if I don't get P, I will be happy with almost the same salary y as D, but will try to bend the rule from 4 years to just 1 year? So it will be like a visiting position with less salary, of less time period, but I will like to be treated like a Ph.D. student (that means less independent research, more learning compared to a postdoc). Will that be a ridiculous thing to try? So, I will be somewhat like an advanced Ph.D. student but not expert like a postdoc and so I am willing to negotiate with the salary, I won't need another Ph.D. since I will have had one(if they give another, fantastic!) Do you know whether it might work or create complications enough so that the hiring committee will be offended? Should I try to send an e-mail explaining this situation and see whether they will negotiate with me on this?
Thank you very much in advance!