I have the following in part of my .htaccess file:
# the following prevents display of the filetohide file
<files handler.php>
order allow,deny
deny from all
</files>
<files submit.php>
order allow,deny
deny from all
</files>
Can multiple file specifiers not be done within a single set of tags, i.e:
<files submit.php|handler.php|otherfile.txt>
order allow,deny
deny from all
</files>
Could you please try following, if this helps you for multiple file names with different formats(I am yet to test this but written this based on regex).
<files ~ "^((submit|handler)\.php)$|^(otherfile\.txt)$">
order allow,deny
deny from all
</files>