The main issue you run into with shortening the stem is a weight distribution problem. One of the managers at my shop has multiple certifications in fittings and has been teaching me alot about it. I was amazed to find how important it was.

Notice that many of the pros use a long stem on the smaller bike than you or I would use. The trick for us is to find the happy medium between comfort and performance.

I would suggest to get a new bike, used if on a budget, that would not require you to run the stem in the danger zone, beyond the min. insert. (its put there for a reason). I wouldnt want you to get hurt.

You may want to look into a comfort road bike like the retired Trek Pilot, or a Specialized Sequoia. Many manufacturers make frames with higher hand positions and can help you find what fits you.

Make sure that when you get fit is done by someone that has some experience, and to not go too short on the stem. Otherwise you will be messing with the handling on the bike.

Hope you find what you are looking for