I find that if the drops are high enough to use for a lot of the time that they are then too high for sprinting and other max efforts. It also makes the tops too high to be comfortable climbing on. So effectively I would be losing useful hand positions.

Saddle angle nose down a bit perhaps, but it should not impact height much unless you are making a much bigger change (like from Road to TT position). The biggest fit consequence to lowering the front end is a more acute hip angle at the top of your pedal stroke.

Everybody has a natural comfort zone for this angle. And getting too acute can cause a number of issues, among them loss of power. This may also be why the bike "feels smaller". In the TT/Tri world hip angle is a major fit variable, the adjustment is to move the seat foreword as you drop the front, opening up the hip angle. You see riders naturally doing this, riding on the nose of the saddle when they get lower.

You might try moving the seat foreword 10 to 20mm. This will likely change the seat height so you will need to reset that.

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.