Thank you all for your responses.

My bike is a cheapazoid Giant Boulder, and I can straddle the top tube just fine. I have straight bars on it and I seem to ride with my arms pretty straight, although not locked.

I just want to keep the bars at the height I have and shorten the reach.

"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."

I have a variable stem already, but from what you all are saying, I don't want to reverse any stem, obtain a 0 mm (extension) stem and probably need stem risers to keep my bars at the present height.

Then again what sounds easiest at this point is to go the new handlebars route: bars with some sweep/rise angled back towards me to keep the height the same sounds like it might just work.

Thanks for the advice.