I have also noticed odd behavior with NVDA and Word 2016. My issues are
similar to yours in some ways but different in others.

I am not a Braille display owner and so I'm only using speech.
Specifically, I'm using NVDA 2016.4 on a Windows 10 Pro machine. With
other editors, such as Jarte, the responsiveness with NVDA behaves as
expected, with no unusual pause when using arrow keys to move the caret
or cursor.

With Word 2016, there is a more noticeable delay from the time I press
an arrow key until the time I hear the character announced. It is not an
unreasonable delay but is just noticeable to be annoying. Turning off
Word's visual features, such as animation, did not help. Disabling
graphics acceleration, or words to that effect, made no difference.
Oddly, what seems to help is if I set the window to a restored state,
rather than a maximized state, and putting Word into draft mode. These
steps seem to help with performance.

When I am navigating the Word options dialog via pressing the tab key,
there are times when I notice a pause of around 2 seconds from the time
I press the tab key until the next option in the dialog is announced.

Finally, when I press ctrl-S to invoke the Save dialog, NVDA is silent,
even though the save dialog now has focus. If I do something to move
focus away from and then back to the dialog, NVDA reads the dialog. As
an example, if I press the alt key twice, NVDA then behaves normally.
This does not occur with other computers I have used and so it could be
some weirdness with my video card or graphics card but these are just
guesses. I am not writing to complain or to knock NVDA, as it is my
screen reader of choice, but just wanted to share my experiences and to
see if others who have experienced this might have found other workarounds.

David Goldfield,
Assistive Technology Specialist

Feel free to visit my Web site
WWW.DavidGoldfield.Info