Perform two keystrokes successively in AppleScript

Well, hard to prove a negative but, as the question you linked to yourself says: you are holding the ⌘ and ⇧ keys down when calling the script. It can not ignore them. Apple script is scripting, and much closer to GUI scripting than to applicative scripting.

I cannot offer any other idea than in the answer to the question you sent: just add a slight delay so that you release the keys before the keystrokes are sent.

delay 0.2

Adding > /dev/null 2>&1 & to the end of the do shell script command should work. This redirects the stdout and stderr of the do shell script command to /dev/null and runs the shell script in the background, meaning that AppleScript no longer needs to wait for the command to return stdout or stderr before the AppleScript script can finish. That means that it finishes and can be run again much more quickly.

You also shouldn't need the try handler at the beginning. The following modified script should work:

set currentVolume to output volume of (get volume settings)
set volume output volume (currentVolume + 2)
-- play volume changing sound at new volume
do shell script "afplay /System/Library/LoginPlugins/BezelServices.loginPlugin/Contents/Resources/volume.aiff > /dev/null 2>&1 &" 

I got this tip from MacScripter (an excellent resource for AppleScripting) in a post about running multiple instances of a shell script.