What flashvars can I use or put into the config xml so that the player doesn't show the 'Email' and 'Share' options at the end of playing a video file? It may be obvious, but I'm not finding it.

<viral> is already set to 0

You can't remove email or share only.
You can remove "menu" button, so all menu will not be available.

I did that, but email and share still show after the video plays. I'm using the player to run videos inside a members area, so emailing them and sharing them won't really work. So, I'd rather not give people the option.

Unfortunately (if I remember) there is no option to show "nothing" when video ends.
One flashvar maybe worth mention "repeat". If set to "1" - forces video to replay and not show any menu.

From some time I stopped developing 4.x version, don't even remember all options.
I focused on new player version which is in very advanced phase.

Sounds good. Thank you for the info. Maybe I'll set up a playlist and just play an image file after the videos for a very long time or something. At least until it is an option to have nothing after.

Well I can't do anything with the current source, but with your suggestion in new version I will add option to show only "replay" button when video (or playlist) finished

Also emailed on this, however this is critical for us. Can not launch within my organization with those viral / social features enabled so am stuck until it's removed or going back to the old player. Note everyone really likes Nuevo Player so hate to go there but can't hold up life.

You really sound weird.
Every user can review player and multiple demos before decide to purchase, also there is all flashvars list showing exactly what is possible to set, finally everyone can contact us can ask before buy.
Other story is why do you look for Nuevoplayer if you want to hide most of features?
If you need very basic player - there are plenty of such players around.

Whatever, we have new version of the player ready, which soon will be released, so any request concerning old source is aimless.