The answer to your issue is right there in your post. If you boot with the drive open, the dualboot.xbe boots directly to the gamesave xbe (MXM). It does not load nkpatcher or a bios loader, so anything you run from the MXM menu would need to be signed (boxplorer is signed which is why you don't get an error when using it). Your best bet would be to boot without a disk in the drive. Then launch games/apps from your dash.
An alternative would be to modify your dash to not load the default.xbe from the dvd drive. This will stop backups from loading when you power up with them in the drive. It also allows for IGR to reset to the dashboard, rather than to the disk in the drive.