Yesterday, I was told I had a cultured English accent. Apparently I sound well-read, whatever that means. After thinking about it, I realised I actually had different accents for different people. And the reason why I sound cultured perhaps comes from the fact I went to university, but I think it is also to do with the fact that I have a lot of friends with various levels of English skills. In other words, I've had to adapt to different people. But, interestingly, if I move away from the city and into the suburbs (I live in Sydney's Inner West in Australia) and hang with people who sport a more 'urban' accent, I tend to change the way I speak. I use more Aussie ocker (colloquialisms) than I would if I lived in the culturally diverse Inner West. And I believe that all English speakers, whether native or learned, have ways of speaking English.
In regards to your story being rejected for possible inauthenticity, I'd suspect that it is because you have winged it. With stories that are set in certain time periods, I'd highly recommend researching and matching fully, rather than mixing it up in your own way. But kudos to you for writing something like that. It's absolutely difficult to write in a specific language or accent.
Keep up the good work!