If it were my house, I'd want the flange at the standard 12" from the finished wall...then, I'd have a huge range of choices at any time in the furure (or now). If you moved it closer to accommodate your preferences for a specific toilet, you'd forever be stuck should you wish to remodel down the road.
Why the Drake ends up with a larger gap than many, I don't know. It is a good toilet...I put two of them into my mother's house. If I had to do it today, I'd seriously consider the Drake II for the neater bowl wash and lower water use. Toto just announced a new toilet that only uses 1g! Not sure when you'll actually be able to buy it, but if you were in an area where water was particularly dear, it sounds like a great choice.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013, 2014
Actually, 11.5 would do that.
If you can get past the styling of the Promenade and if you fit on a round bowl. If you can spare 1 3/8" you can get the Aquia III which looks better, has an elongated bowl and has dual flush. Unfortunately, it's not available with Sanagloss.
I finally mounted the Aquia and have been using it a couple of weeks. I'm very pleased with it's looks, sounds, ergonomics and performance. Compact but with no dingle-dangle! Best toilet I've ever had.
I ended up mounting the flange at 11 1/2" which worked out perfectly and kept wasted space to a minimum.
One thing I was not aware of - The Aquia requires two mounting blocks be mounted on the floor behind the drain flange. This was almost a big problem as I had already installed floor heating wire that was about 7" from the flange. Fortunately I had taken pictures of the heating wire install before tiling over and one photo was taken from a very good angle that allowed me to determine the screws for the toilet mounting blocks would miss the wire by at least 1/2". Too close for complete comfort but I crossed my fingers and drilled away. Not a problem after all. Also, the Aquia is not compatible (as far as I could tell) with the new waxless style drain seal. But this wasn't a problem - I just used the traditional wax ring. The Aquia is designed so a small rocking motion of the toilet will not gradually work the wax seal. Not that the toilet should be installed such that it can rock but the system does seem less prone to fail over time.