Suggestions:

1. Get a bike that is the correct size
2. Get a shorter higher stem - as long as the steerer clamp and bar clamp are the right size then the stem will work.
3. Get a bar with some flare (Randonneur bars) or shallower drops to give you more useful hand positions
4. Get a bike designed for an upright riding position - a hybrid or 'flat bar road bike' or one of any number or 'relaxed geometry' road-sport bikes available.
5. Swap to flat or riser or trekking/butterfly bars (this is usually not straighforward so this would be the last thing I would try)