Sprint Planning with geographically dispersed teams located in different timezones

When working with geographically dispersed teams (where the members of one team are spread across different locations), the team members and I find it rather difficult to keep focused on the phone during the entire Sprint Planning 1 and 2. Even more so when considering the different time zones. As one part of the team comes in right after lunch, the other part is nearly on their way home, while the third part is starving for lunch. In this situation, the retrospectives showed that the quality of the Sprint Planning 2 and the common understanding of the design ideas should be improved. Additionally, I (as ScrumMaster) wished to improve the team members' communication and their participation within both Sprint Plannings. For reasons of seniority, experience and cultural differences, it was always the same few members who participated in the discussions. Noticing a possibility for killing two birds with one stone, I changed the set-up of the Sprint Plannings - despite some team members complaining about long planning sessions and that Scrum was creating too much overhead ;-). So I changed the Sprint Plannings in such a way that they would not be held within one day, but split into two different days, using the morning in Europe for the three hours overlap of working time. That gave us the opportunity to use two full hours for the Sprint Planning 1 and 2 on each day. Furthermore, to increase the participation of the team members, I asked all members working in the same location to hold their own smaller version of a Sprint Planning 2 on the day or morning before the session with the whole team. By doing so, I automatically created some competition amongst the dispersed team to come up with the „best“ solutions and share them with the others. This was particularly interesting, as I had not split the pulled stories for the Sprint Planning 2, but instead asked every location to put forward a design for every story. Now that we had three different solutions on the table in the Sprint Planning 2, the team was able to discuss which one would be preferred or which combination of the different design solutions made the most sense. Since all members had participated in the design of a solution, their involvement and the variety of possibilities for implementation clearly increased. At the same time, the meetings were not as long and stiff anymore. Plus: The additional time now available after the Sprint Planning 2 or before the Sprint Planning 1 could now be used for working through the feedback from the review, continuing on the development of technical topics, or even refactoring ;-) What advice do you have for working with geographically dispersed teams?  See also the interview series by Stephanie Gasche about internationally distributed Scrum-Teams.