I submitted a short 10 page combinatorics paper with a couple of small results, to one journal, and got a rejection in 5 weeks with the referee stating he/she has read the entire paper and that the arguments are simple.
After this, I submitted this paper to another slightly lower tier journal without mentioning this prior submission, and it has been over 13 months. I contacted the journal's editorial staff (not anyone in the editorial board; there also doesn't seem to be an option to contact the editors directly through the submission portal) after 11 months and they said new referees had been invited then.
I do not consider this paper to have significant results, but would have hoped to have heard about this by now. The journal's online portal also doesn't give an option to withdraw the paper. In this instance, is it acceptable to contact the editor by email and request a decision soon?
Edit: There is another separate short and not very significant 11 page mathematics paper where I prematurely asked the handling editor 4 months after submission, about whether the paper is with a referee and the handling editor was very kind to get back to me stating the paper was with a referee. I sent him another request after 14 months and he apologized for the delay and said they are expecting a report 'within days'. A few weeks later I got a rejection with the referee in his review of a few lines basically only commenting on the first two lines of the abstract. This particular paper was a bit poorly written, however here there was seamless communication from the handling editor I was very grateful for, but even then the process didn't feel right in the end.
In such circumstances, beyond making sure the paper is written as well as possible, what recourse does the author have when the refereeing process seems to be taking a long time?
As an aside, it is a very different culture, but I regularly referee for one of the handful of respectable expository journals in Physics and the editors start to ask for a report within a few weeks, and it is not that I don't read entire short papers carefully while still being able to submit a report in a few weeks, except a rare instance where parts of the paper look very difficult to follow or not suitable for publication in which case I make it a point to let the authors know about it as soon as possible.