I view bar height and reach in terms of location along the steerer tube centerline and horizontal. (Not right angles I know and that probably drives some nuts, but the fact was - before threadless steerers - racing bikes all had horizontal quill stems of increments of 1cm and could be raised or lowered along the steerer.)

I disagree fundamentally with squid puppet. I find that shoulder location is key torso comfort and position on the bike. I like a comfortable bend in my arm. That sets the distance from my shoulders to the HBs. But I can pivot my arms. In practice, I find little difference between my HBs higher and further forward or closer and down, as long as that distance to my shoulders is the same. Very conveniently (for me at least), along say 6" of that arc which is almost a straight line, the slope of that line is 2 cm horizontally by 1 cm along the steerer. Yes, a very bastardized measuring system, but for application to bicycles, very practical.

Now, as I get older (or if I want to set up a bike as a "comfort" bike, I just raise that line. The slope doesn't change. (Yes, as I rotate my whole position back for the comfort bike, the slope does change some, but the effect of the slope change over 6" is second order and I ignore it.)

It sounds like you want that line raised. Flipping the stem wil do that (unless it is a 0 degree stem (90 degrees from the steerer). Since we don't know what your stem angle is, speculation on the effect of flipping it is just that. A 5 degree stem would have a small change in reach and height, a 45 degree stem would have a radical change.

Ben