I just got a road bike and I set the saddle set properly (height and fore/aft) and then position my hands on the brake hoods. Then I bring one hand back and/or up to where my arm is not locked and feels relaxed. Then measure how much I need to come back and/or up to get there. Not very scientific but it's a good starting point. A bike shop may be willing to loan you some stems if you agree to buy one from them.

I'd try flipping the stem now to see if you like the higher position better.