Quick update:

After a week riding with my lower bars, I think I've adapted and it no longer feels like I'm riding a kid's bike. The one inch drop did feel like a huge difference at first though.

Other observations:

My back and shoulders actually feel a bit better now. I'm a little bit more stretched out (8mm according to Stem Comparison Tool | yojimg.net) and my arms a little bit straighter, but still be a comfortable bend at the elbow. As with my other bike, I actually find having the bars lower stops me scrunching up my shoulders and forces me to relax my arms to lengthen them.

Getting on the drops does make the bike feel small as though I'm quite far forward over the bar. I tend to scoot back on the saddle a little to avoid the "going over the bars" feeling when braking. However, my back is quite flat, and it feels aero.

Climbing out the saddle is maybe a little weaker and less controlled than before and I need to bend my torso further forward to reach the hoods. I think I'm at the limit of bar height - any lower and I wouldn't be able to control the bike well when out of the saddle. I have longer-than-average legs for my height (34.5" inseam, 5'9.5" tall), so I guess this means my torso must be shorter-than-average - so it's harder to reach the bars unless I bend over.

As many of you have suggested, I have adapted. So far I haven't seen any noticeable speed benefit on my commute, but I'll record my rides over the next couple of months and compare data.