Greg:
There is no need to try the CharacterEncoding->"Unicode" as this only proves that one can export the same data and by chosing that character encoding the file will be larger (double byte). But in your case it was the quoted and unquoted fields that made a difference.
I would like it if the CSV issues on all systems would be put to bed, but CSV is not yet a true standard (?). [Not looking for a debate]. Many don't implement it well not just on export but on import. But I believe that WRI is doing the export correctly, put quotes around fields. If one reads the RFC for CSV and many other notes and opinions on CSV, it is hard for me to see how one would not come to the conclusion that the safest way to protect fields from confusion is to wrap them in quotes and worry about types later.
Also note that the qoute character can be substituted and escape characters can be used. There are many EDI systems (formats) that indicate the record, field, escape separators and delimiters in a header/init or first line of file being transformed/consumed. So CSV is not different just badly implemented in many systems.
Now WL provide ways that you can create you own import/export converter. So I think that could be the best approach. You want to export your CSV without quotes. I am not certain of all the pitfalls (if any). When time permits I may come back with code examples.