You are right, if I build EABI, my application runs outside of the chroot, and everything works. On the other hand, my SDK was not outdated: I was just using the latest version found on the official site (http://pocketbook-free.sourceforge.net/en/sdk.shtml
) of the non-pro SDK. So the solution is: for 360+ use the pro SDK!
It is finally clear that the chroot is a buggy backward-compatibility trick for binaries produced using the non-pro SDK. The monitor application (or whatever menages the applications menu) runs shell scripts and EABI binaries outside the chroot, and OABI binaries chrooted.
Thank you for your help,