Could I achieve the same results by swapping stems or adjusting handlebars, etc. on a H2ead of searching for a h3 frame?
You can to an extent, and it works both ways; i.e., you can get an H3 frame and duplicate the H2 fit as well by changing out stems and spacers.
I'd go for the H3. You can get lower on the bike without having to resort to weird fixes (like adjustable stems) more easily than raising the bars to fit you. My discovery that I needed a taller head tube required buying a new frameset, since the original frame's head tube was way too short.