For this context, I actually highly recommend iDoneThis.
Basically, iDoneThis sends an email to everyone on your team (so in this case, everyone on your 3 Scrum teams) and every person writes a quick reply to the email about what they've done that day (you can have it sent out whenever you want). The next day, iDoneThis sends a digest to the entire team with those replies.
It's fantastic; everyone can see the information, but if something specific needs to be addressed, those people who it applies to can deal with it between themselves. In this way, it doesn't waste others time who aren't involved. Those people can then include an update on the next day's email if needed.
I did find that it wasn't efficient for smaller teams. For example, we used it on my 6-person team and loved the idea, but found that we could just easily have a short daily stand-up in addition to a chat client. But for a large team, I bet this will be invaluable.
I think it is still important to have occasional all-hands team meetings, but for an everyday update, this is perfect.
It's not free but it's only $5/member/month, and worth it in my opinion.
Side note: this is also great to just use as a tool just for yourself (a "work diary", if you will). For this purpose (1 person), it's free. This is how I use it now and love it.