I dont think a 5'3" female rider will fit onto a 19" frame. The modern trend for road bikes is to allow more crotch clearance (about 3"), but to maintain the same length. This means that a small rider may be able to clear the top tube like a 1970s racer, but the frame will be way too long.
Off-road bikes need even more crotch clearance (4-6"), and these bikes should be a little shorter in length, since aerodynamics is not critical.
A CX style 531 frame built for MTB wheel size would be ideal, but dont discount MTBs if you want a ready built frame. Quality mid-range Al or steel MTBs are not overweight and are easy to pick up used. The wheels can be very strong and light, and narrow CX or touring style tyres (1.5" wide) would be fine. If you dont like the heavy MTB forks, then swap them for a set of springy 531 for much improved performance.

A triple crank would be the best gearing solution. Short legs deserve short cranks (probably 160 to 165mm). My local bikeshop has a beautiful TA triple chainset in 165 for a mere £30, its is normally £160. If building from scratch, you can use short cranks to advantage to build a bike which is lower and shorter.

You could probably simplify your shifter problems by sticking with straight bars and bar-ends, or if you need multiple hand positions, butterfly bars. Standard drop bar shifters are not built for small hands.