Hi Tom.

QUOTE:
I set everything in the com_export_content directory to 777. I also unzipped export content locally and uploaded FTP to my server.
Still no change. I get the same result - 500 internal server error.

Ok we know it's not a permission issue and if it works on one site and not the other it must be something to do with the server setting.

Make sure that it is not a file ownership issue.

Is iconv library enabled on the server where you are having the trouble?

I would look at the server that is working and compare it to other and see what is different e.g. php settings.

Then ask your host to make the adjustments or if you have control make the changes needed.

QUOTE:
Do you know of any other Joomla extensions that export content?

No not that I'm aware of.
There are others that will move the whole site but not content only and will not allow you to move into existing site that is already populated with content.

Please post back with your results as it may help others.