Assuming that you don't have a really deep baseboard, allowing for some differences in molding (because the clay shrinks when fired; consistent clay is the key to consistent size), one can usually put the thing on 10-7/8. That would give you essentially no space between the toilet and the wall. If you're thinking 11-1/4, that will give you what you want: about 3/8" behind the toilet.
Of course, since you demo'd the bathroom already, I assume you removed the toilet already. Just put it against the wall (or however far off the wall you think looks nice) and measure from the wall to the center of the holes for the closet bolts. Now you know for sure the measurements for your particular toilet.
However, I'm not sure that you want to stick the next homeowner (or yourself) with an insufficient, non-standard rough-in. Eventually, that toilet is going to be replaced; indeed, someone could inadvertently break it, and you deprive yourself of the opportunity to put in, say, a Drake II, which requires significantly more room than the Drake. Relatively-few toilets are going to fit on 11-1/4", and who knows what will be available ten years from now. You are sticking yourself or the next homeowner with a potential bugaboo that will be expensive to repair/replace.
Regardless, you've got a great toilet; we all love our Drakes.