Markets for mainstream/contemp?

Since no one else has chimed in, I'll offer my perspective. Most of the markets I researched for short fiction were literary magazines. There are mainstream ones for science fiction, fantasy, and horror but you won't find a lot of those on newsstands. The literary mags tend to have low acceptance rates and take a very long time to respond.

Try searching Duotrope's Digest. It's now fee-based for full use, but I think you can still search for free.

There's nothing wrong with fee based data bases. Sometimes you have to pay to play, and it's a ridiculously small investment in your business, and if you really want to sell short stories, you must treat writing like the business it is.

Other than this, read the magazines you want to submit stories to. There is no other way of knowing exactly what they want.

It's better to start with the small press magazines, rather than trawling through the magazines on news stands.

I don't know what genre you're writing but there are tons of small magazines and online based platforms alive and kicking in all genres. Some of these have enormous kudos for the writer and many have published big-name authors at some point.

Many successful writers build their reputations in the small presses before finding fame and fortune.

The underground lit-scene is currently one of the most exciting areas in any of he arts, and small mags catering for science fiction / fantasy / noir / crime, are positively thriving.

A free database is: http://thegrinder.diabolicalplots.com/

The part of this post that concerns me is the idea that your work doesn't "feel literary." I wonder if you're being fair to yourself, though I can't say without seeing the work, of course. Modern realist literary fiction is typically pretty "slice of life" (a phrase I actually think is way problematic). Try reading work that some of those markets are putting out and see if anything you see looks like what you do.

I think the line between literary and mainstream/contemporary is pretty blurred if there even is a line when it comes to what is being published in the journals. Try reading more of the journals, and I think you will see what I am talking about. There are a lot of stories in these journals that are very edgy and less language driven. You can find stories like that even in The Paris Review which is probably the top literary journal. The more you read, the better you will be able to gage where your stuff might fit.