Just so I'm heading down the right track: my back and shoulders should kinda roll forward, as if I were slouching, right? And my hands and arms should be carrying my upper body weight, but with my elbows at an angle, so that it's not the bones carrying that weight, right? I'm trying to both dial in my bike and figure out this posture thing. Currently, I'm feeling a bit weird in the drops: I feel like my thighs are hitting my ribs, despite having the seat perhaps too high (if I put my heels onto the pedals, I'd have to rock my hips to pedal). I'm not used to a road bike, but I'm liking the speed of it.

Are you an old guy?

raise your bars.

Young guy, but with a spare tire in the middle that I need to lose. I'll check on the bars; I haven't gotten the stem to break loose yet on my old bike, so maybe I can raise 'em and maybe not. I think the bars are about 1 to 2 inches below the saddle, but I haven't measured that (yet).

I'm so inflexible. It takes me a while to stretch into position each season.

Maybe yoga is the answer.

Re-start the posture thing:
1) Raise the bars so the tops are level with the saddle.
2) Rotate the bars up so the ramps are almost level with the ground - or totally level.
3) Adjust the saddle so you don't rock.

If you are riding with your elbows straight, move the saddle forward. Don't be too concerned with Knee Over Pedal unless it bothers you. If you are still having discomfort while in the drops, measure your drop distance on the bars and get a set that is 5" or less. For maximum comfort, the drop grip should almost clear the top tube.

In fact, for people with these complaints, I suggest a read of Rivendell's Grant Peterson. His idea of riding a bike may be refreshing.

like this:
https://i16.tinypic.com/61t6z28.jpg
or this:
https://i11.tinypic.com/4lh321i.jpg

I attempted to break loose the headset last night, but it didn't want to move. I unscrewed the allen bolt in the stem several turns, and gave it a few taps--I didn't see it move. I'm a bit reluctant to wail on it just yet, as I'm afraid of what I might break; and it is currently a ridable bike, albeit not as comfortable as I want currently (or think I want). I did measure it, and there is about a 3cm difference in height from the top of the handlebar to the top of the seat.

I did move the seat forward, but wound up with the nose about flat--if I tilt it up as in that last photo, it just doesn't feel quite right. I suspect I could raise the nose up if the bars were up more, but where the handlebars are fixed for now, I think the angle is about right, and I need to figure out how to support my upper body better. I may need a seat that can slide forward more.

I think I'll try some more rides, and see if I still find it uncomfortable or if I start to like the position better. I honestly haven't ridden that much.

I don't know what saddle you're using. Obviously, mine are Brooks'. They work best for most people when tilted slightly up. The original saddle on that Specialized road bike in the first pic was a Milano. Cheap, but decent out to about 40 miles. It usually feels best when level. Whatever saddle you use is really immaterial for now. You just need to get comfortable with what you have, right?

As far as breaking loose that stuck stem: You can turn the bike over and spray WD-40 inside the head tube to soak the tapered wedge and get it to soak the stem quill. In the end, it might take a good whacking to bust it loose. Just make sure you hit it square-on, not a glancing blow.

A bar that is 3cm lower than the saddle would bother me after about 15 miles. Good luck.

The saddle is a Sella Anatomic, which has probably seen better days--the covering on the sadle is only attached front and back, not on the sides so well. In the right spot, it's been fine for the 12ish miles that I'm capable of. If I were to be doing more, I'd seriously look into a Brooks; they seem to have a dedicated following. Anyhow, I think I just need more saddle time, while carrying the tools to make adjustments as I go.