Ive seen a guy with a reversed stem. He seemed quite happy with it, but he was also wobbling all over the road.
I would not recomend it. Short stems make the steering more responsive, and negative stems will upset your ability to lean into corners and generally balance the bike.
You can get variable stems quite cheaply. Often the come on mid-range hybrid bikes, and people replace them with lighter, stiffer fixed stems, so you may be able to pick one up cheaply.
You probably do have a bike which is too long. When you go looking for a solution, there are some pitfalls to look out for, but generally, you would get a make with a short design, + a smaller size. Dont forget the larger sizes of womens bikes as an alternative.
Short stems are available at reasonable price from 3TTT.