I could be mistaken, but I do not think the family was on the Baltic to Black sea voyage. They normally used the Imperial Train from St.P. and back, just used the yacht for cruises around the area. The now famous Romania visit was one of those stops.
As for stops on the former route, I do not know how long the Standart could sail before needing refuel and provisioning. Douglas probably does. But logic suggests that Barcelona and perhaps Greece ? I have read that various family members used this opportunity to "hitch a ride" to various spots along the way, perhaps Biariitz, Monte Carlo, etc. That way, they did not have to deal with N&A and their brood.