Yikes, OP! I'm a little under 5'3". If I had a horse 16h I'd need a fire ladder or a trampoline. My personal favorite is a picnic table, but they can be a bit hard to come by out on a trail.
I have wondered about some of the gadgets...drop-down stirrup or step stool. Seems like there are issues with these so never tried them.
Mounting a horse takes a certain amount of agility, coordination and strength, no matter how you look at it...and no matter what your size. One of my concerns has always been to put the least amount of pressure as possible on the structure of my horse's back while getting myself safely seated. On the trail I always look for a rock, log, stump, or low spot for the horse.
So, I guess, short of gymnastics classes, make sure your horse is trained to stand beside whatever you need to use.
Sorry...this probably isn't very helpful. I wish you success and I fully understand the issue you have. It's frustrating.
If you ever find yourself in a fair fight, it's because your tactics suck. ~ Marine 1SGT J. Reifinger