Digging a little more I found out that rather than a patch what really needs to happen is for eaccelerator to be compiled with --without-eaccelerator-use-inode per the developer. The inode option will be eliminated from the code in future versions as a permanent fix since it would provide no performance increase over no inode if patched to support open_basedir and it doesn't provide a significant performance increase in the first place.
#104 (e-accelerator open_basedir errors) - eAccelerator - Trac
The problem is that easyapache doesn't allow you to specify compile options for eaccelerator. But you can't just patch the compile script because easyapache refreshes it from the cPanel servers every time it runs. So what I did was create an easyapache hook script to patch the compile script on the fly when easyapache runs. Create /scripts/before_apache_make with the following contents and make it executable.
Code:
#!/bin/sh
cd /home/cpeasyapache/src/eaccelerator
mv cpanel-install cpanel-install.sav
sed "s@'./configure', '--with-php-config@'./configure', '--without-eaccelerator-use-inode', '--with-php-config@" cpanel-install.sav > cpanel-install
rm -f cpanel-install.sav
chmod +x cpanel-install