This is actually quite simple, just follow Chirpy's recommendation from the cPanel forums.

1. Create a file called /etc/myaliases with:

postmaster: root
abuse: root
2. In the WHM > Exim Configuration Editor scroll down to the section "DIRECTORS CONFIGURATION" and in the first textbox of that section put:

Code:
mysystem_aliases:
driver = redirect
allow_defer
allow_fail
data = ${lookup{$local_part}lsearch{/etc/myaliases}}
file_transport = address_file
pipe_transport = address_pipe
retry_use_local_part

You'll then have a server-wide postmaster and abuse address that won't be interefered with by users having :fail: Default Addresses.