Sorry your having such a hard time here.
As you know the PowerBook G4 is the last laptop Apple made with the PowerPC CPU chip [http://en.wikipedia.org/wiki/PowerBook_G4|Wikipedia Info]. As such your OS choices are limited and Apple no longer offers help or services this system.
As you have a real copy of Leopard DVD (10.5) you should be able to recover things. As long as the system is functional.
If you can mount the system in disk mode to the other Mac system you should be able to install a full copy of OS manually.
You're right the system you have running will ID the software installer (15") incorrectly (the one in disk mode 17"). To correct for that you need to manually install the OS and install the all of the system libraries. When you get to the installer main screen don't let it install the OS automatically, go into the manual area and expand the sub sections and check off the setting that offers the universal boot option.
Don't forget to bless the HD as bootable under the control panel. If you install things correctly you should be able to reboot your master system (the one doing the work here) and the slave system (disk mode system) should boot your master system. If it does you should then be able to shutdown both and disconnect your systems and restart them, both should then boot up off their own internal HD's.
If this still fails you'll need to setup an external Firewire HD with a bootable universal system and then use it to boot your PowerBook G4 from. Again, go into the control panel and make sure the internal CD/DVD player is the bootable. Then use the installer DVD and try again or copy the external HD system over.