Its most likely the rounded corners that is causing the slow down. Not sure what radius you are using, but having to compute how the text will fit with the rounded corners is much more expensive than when the text frame is a simple box. One suggestion to help alleviate the problem is to break the document up by chapter so that you don't have the end of one chapter linking to the start of the next. When you have a large number of pages with text that all flows from one page to the other, editing text in one page means that all the following ones need to be recomputed. Breaking that cascade of changes from one page to the next will help with performance. One downside is that you'll have to be careful and watch for overset text or blank pages happening at the end of each chapter.
Strange that such a simple style should slow things down. When I started using the rounded corners it didn't seem to make a difference. But you are right — as soon as I took off the rounded corners the typing speed improved instantly. I think I will just take the rounded corners off the object style until I'm done typing in all of them and then reapply them afterwards. Thanks!
(The text boxes are not linked, so I don't think breaking into chapters would help, would it?)