You're definitely correct that getting sychrotron time is hard :(
On the first part though: Yes and no. XRD will tell you about things like strain and unit cell size distribution, so in that sense, you can't resolve a single doping site. On the other hand, if you have a reaction going on, or some dopant diffusing into your sample, synchrotron XRD is powerful/fast enough that you can "film" how the crystal structure changes in real time. That "film" will be a kind of average of many sites, but can still be focused to a relatively small region (don't remember exactly how small off the top of my head, but I believe we're talking nm-scale).