Another idea is a 2 column side-by-side timeline listing the major events in your unit and what was happening here at approximately the same time. So if you are doing ancient civilizations you could have the students include ancient civilizations in the Americas. Or if you are doing the Middle Ages, they would include events from the North American Indian cultures. For example:
I know I have seen these kinds of timelines but couldn't find something online quickly. But if you could locate a ready-made one (I feel it must be out there!) that would minimize your prep time. If you felt it was needed, you could ask individual students to prepare a short presentation about event(s) on the U.S. side of the timeline. Or you could show a video clip. You might also try Youtube.
Perhaps you could do some kind of U.S. history bell work activity. I used to do bell work with a book called Take Five Minutes for Geography and I was hoping there might be something similar for U.S. History. Not what I was hoping to find, but there is one on Amazon called Take Five Minutes: A History Fact a Day for Editing. The 2-3 sentence passages are about U.S. History but not necessarily famous events and they don't seem to be in any chronological order from the sample page. For example, the entry for October 14 is about Theodore Roosevelt being shot in the chest while giving a campaign speech. So you would do that around the time you might be covering ancient Egypt, for example. Also they don't have any punctuation so they would be great if you are interested in a cross-curricular activity with Language Arts, but not if you aren't.
If you wanted to write your own short bell work paragraph, the U.S. History overview article in Wikipedia looks like a good summary of each time period that you could quickly rewrite at 6th grade level. You could correlate them to the time period you are studying in world history. Maybe do a paragraph with fill-ins and a word bank on a one page handout. For that, you could probably do just one per week.
Having students read a historical fiction selection in addition to the work for whatever unit you are covering seems like a bit much, in my opinion. And that's just the reading, never mind if you have them do any kind of follow-up for accountability.
A read-aloud might work but it seems like you want to focus on interesting supplements for your curriculum topic, such as bringing ancient Greece alive for the kids. Also, it would depend on your objective but I'm not sure a read-aloud would have much sticking power unless you simply wanted to stir up their prior knowledge and do a quick oral review. Otherwise you would need to do some kind of follow-up like a journal entry type reaction. With the fill-in paragraph I mentioned above, they would have a handout for reference.
Just a few thoughts! I hope someone will recommend some great video clips! Hats off to you for wanting to undertake this and spend time from your own curriculum.