I got it working, and I found out thanks to your advice of enabling verbose tracing! I love you for that!!

Here is the final code, and output, for anyone else facing this issue.

Code:
#include <stdio.h>
#include <string.h>
 
#include <curl/curl.h>
#include <curl/types.h> 
#include <curl/easy.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <fcntl.h>
#include <errno.h>
#ifdef WIN32
#include <io.h>
#else
#include <unistd.h>
#endif
 
/*
 * This example shows an FTP upload, with a rename of the file just after
 * a successful upload.
 *
 * Example based on source code provided by Erick Nuwendam. Thanks!
 */ 
 
#define LOCAL_FILE      "feed.txt"
#define RENAME_FILE_TO  "feed.zip"
#define UPLOAD_FILE_AS  "feed.txt"

 
/* NOTE: if you want this example to work on Windows with libcurl as a
   DLL, you MUST also provide a read callback with CURLOPT_READFUNCTION.
   Failing to do so will give you a crash since a DLL may not use the
   variable's memory when passed in to it from an app like this. */ 
static size_t read_callback(void *ptr, size_t size, size_t nmemb, void *stream)
{
  /* in real-world cases, this would probably get this data differently
     as this fread() stuff is exactly what the library already would do
     by default internally */ 
  size_t retcode = fread(ptr, size, nmemb, stream);
 
  printf("*** We read %d bytes from file\n", retcode);
  return retcode;
}
 
int main(void)
{
  CURL *curl;
  CURLcode res;
  FILE *hd_src;
  struct stat file_info;
  double speed_upload, total_time;
  curl_off_t fsize;
  // I had to add public_html as a folder, because it said there was no projects directory.  As well as add the filename to the final URL below
  char *REMOTE_URL = "ftp://iss.netii.net/public_html/projects/message/feed.zip";
 
  struct curl_slist *headerlist=NULL;
  static const char buf_1 [] = "RNFR " UPLOAD_FILE_AS;
  static const char buf_2 [] = "RNTO " RENAME_FILE_TO;
 
  /* get the file size of the local file */ 
  if(stat(LOCAL_FILE, &file_info)) {
    printf("Couldnt open '%s': %s\n", LOCAL_FILE, strerror(errno));
    return 1;
  }
  fsize = (curl_off_t)file_info.st_size;
 
  printf("Local file size: %" CURL_FORMAT_CURL_OFF_T " bytes.\n", fsize);
 
  /* get a FILE * of the same file */ 
  hd_src = fopen(LOCAL_FILE, "rb");
 
  /* In windows, this will init the winsock stuff */ 
  curl_global_init(CURL_GLOBAL_ALL);
 
  /* get a curl handle */ 
  curl = curl_easy_init();
  if(curl) {
    /* build a list of commands to pass to libcurl */ 
    headerlist = curl_slist_append(headerlist, buf_1);
    headerlist = curl_slist_append(headerlist, buf_2);
 
    /* we want to use our own read function */ 
    curl_easy_setopt(curl, CURLOPT_READFUNCTION, read_callback);
 
    /* enable uploading */ 
    curl_easy_setopt(curl, CURLOPT_UPLOAD, 1L);
 
    /* specify target */ 
    curl_easy_setopt(curl,CURLOPT_URL, REMOTE_URL);
 
    /* pass in that last of FTP commands to run after the transfer */ 
    curl_easy_setopt(curl, CURLOPT_POSTQUOTE, headerlist);
 
    /* now specify which file to upload */ 
    curl_easy_setopt(curl, CURLOPT_READDATA, hd_src);
    
    /* specify username and password for ftp */
    curl_easy_setopt(curl, CURLOPT_USERNAME, "username");
    curl_easy_setopt(curl, CURLOPT_PASSWORD, "password");
 
    /* Set the size of the file to upload (optional).  If you give a *_LARGE
       option you MUST make sure that the type of the passed-in argument is a
       curl_off_t. If you use CURLOPT_INFILESIZE (without _LARGE) you must
       make sure that to pass in a type 'long' argument. */ 
    curl_easy_setopt(curl, CURLOPT_INFILESIZE_LARGE,
                     (curl_off_t)fsize);
                     
    /* enable verbose for easier tracing */ 
    curl_easy_setopt(curl, CURLOPT_VERBOSE, 1L);
 
    /* Now run off and do what you've been told! */ 
    res = curl_easy_perform(curl);
    
    /* now extract transfer info */ 
    curl_easy_getinfo(curl, CURLINFO_SPEED_UPLOAD, &speed_upload);
    curl_easy_getinfo(curl, CURLINFO_TOTAL_TIME, &total_time);
 
    printf("Speed: %.3f bytes/sec during %.3f seconds\n", speed_upload, total_time);
 
    /* clean up the FTP commands list */ 
    curl_slist_free_all (headerlist);
 
    /* always cleanup */ 
    curl_easy_cleanup(curl);
  }
  fclose(hd_src); /* close the local file */ 
  getchar();
  curl_global_cleanup();
  return 0;
}
And the output

HTTP File Upload Libcurl-log4-success-jpg

libcurl did the rest, as it found it was passive mode, among other things.

Thank you so much for your help!