If it feels good when on the hoods but that moving to the drops is uncomfortable, perhaps you could use a shallower drop bar. What that means is that the distance from the ramps (the part that bends forward from the flats) to the drops is shorter, so you don't have to reach as far to get to them. Often, bars with shallow drop have lower reach as well (i.e. length of ramps), so the hoods move in a bit closer; this type of bar is called a Compact Bar.

Of course, you may have a compact on already; I don't know. Probably you can look up the name and model of your bar and see the measurements, and compare them against some of the compact options, which have numbers like 79mm reach and 125mm drop.

A new bar can be had quite cheaply, so it may be worth trying, particularly since it does not sound like the frame is troublesome; in fact, moving up in size will likely increase the saddle/bar distance (or Reach). That's not absolutely true, but generally is.

The Giant is in the compact frame geometry camp, but whether making a move to a traditional geometry frame makes sense is an question that needs more input. Ideally, some pics of you on the bike are needed, but at a minimum, a better description of how you feel about the bike fit is needed. In any case, you'll want to take a look at how you fit on the Giant before determining which angles and size you'd want in a new frame, because there would be little point in duplicating reach with a new frame in exchange for a taller seat tube and level top tube (which is basically what traditional geo is).

Can you tell us what length/rise stem you replaced, and what size you replaced it with? How did that change affect you in relation to riding with your hands on the hoods? On the tops?