How to keep them short: Don't disseminating status or solving technical problems. Do that after.
With 60 people in your Scrum Teams you would likely have between 7 and 10 Teams that all meet individually. It would be impossible for your two Project Managers to attend all of the Daily Scrums and you should trust the Development Teams to bring the relevant information to your attention after the meeting.
Daily Scrum - The purpose of this meeting is for the Development Team (3-9 people) to get together and understand what they still have left to do and to update their plan. There is really no requirement for a Project Manager to attend the Daily Scrum except as an observer and any information that the Development Team thinks needs to come to the attention of either the Scrum Master or the Product Owner is up to them.
Scrum of Scrums - Each Development Team should elect a representative to attend the Scrum of Scrums to allow the same information to be passed between the Development Teams so that they can minimise dependencies and make sure that all of the Development Teams have all of their work integrated and tested by the end of the Sprint. Again this is about the Development Teams themselves and not about Project Management.
That all said, you can have as many other meeting that you like about whatever you like outside of those two specific instances.