After trying several different User Agent add-ons, I finally got Netflix to play.
Unfortunately, the User Agent that worked (for me) isn't the most user-friendly.
This is the one that worked for me...and it works on both 64bit and 32bit installs...
https://addons.mozilla.org/en-US/firefox/addon/custom-useragent-string/?src=searchAfter installing it, click its icon on the tool-bar, and click Settings.
In the page that opens, look under "Select Desktop Google Chrome UserAgent String" and scroll down and click the last entry under that heading; which is...
Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/46.0.2490.71 Safari/537.36
Now scroll down the page (not the section where you choose the UserAgent), and click the + sign.
That will add the User Agent to the browser.
Don't be deterred if you get an error message or blank screen on Netflix at first. I had to reload the page a couple of times before I was able to watch a video.
Edited to add: While this allowed me to watch Netflix, it's using an outdated version of Chrome in its string; therefore, you will get some warnings on other websites that you're using an old version of Chrome and need to update. So...the one good thing about this particular add-on is that it's easily turned on and off. So...just turn it on to use Netflix and turn it off everywhere else.