I'll try to keep it simple. Its not just about hand size. I wear a size L women's glove.

Its about flexibility and torso/arm length. You need to be able to reach your bars with a bend in your elbow, not locked out as you describe. There are two ways to bring the bar in, One is to shorten the stem one is to shorten the bar (reach not width now). I don't know what the reach is on your current bar, but I threw out same names of bars know to have relatively short reaches. Turning the bars up and repositioning the levers may also help, but then you have to be sure they don't effect how your hands feel in the drops.

What I just learned though, is how varying the drop can help. My new bar has an ususually shallow drop. That means I don't have to bend as low to reach them, which is better for my body.

What I suggest is, going to shop that may even have these bars already mounted on a bike. We started by putting another bike in a trainer that had the bar I was considering, so I could get a first impression. When it felt right, he mounted one on my bike, and set about varying the position of the brake levers until it felt perfect. Now, this was part of a new bike purchase fitting, so I probably got more attention paid to me than on a retro-fit.

But, everything I hear you saying is that you'd like your bars a bit closer to your body. The shims are about making the levers be closer to the bars when you are in the drops which is a separat but also important issue (a cheap $10 fix).