How to retrieve a list of fields, similar to what is available at
admin/reports/fields, but so that I can have them in an array that I can stuff in a select dropdown.
You should use field_info_fields(), which returns an array containing information about all the defined fields. Its output is similar to the following one.
You can also use field_info_field_map() it returns a lightweight map of fields across bundles. field_info_fields() also return fields list but its document suggesting us "Use of this function should be avoided when possible, since it loads and statically caches a potentially large array of information.".
The function only returns active, non deleted fields.
$field_list = field_info_field_map();