I couldn't use the File Download SB, as it requires the file to reside on the same domain.
After rebuilding a couple times, I was able to get it working. I think the issue was I had my count column in my database set to default: NULL and I had to change it to default: 0 or 1 for the increment to begin.
...and the increment value had to be:
<?php echo $row_rsDownloadCount['downloadCount']+1; ?>
<?php echo $row_rsDownloadCount['downloadCount']++; ?>
for some reason.