I've gotten FCP 4.5 HD to run on several G3 based Macs, and the process is quite simple. This procedure uses FCP4, but is the same for 4.5.
1. Pop in the FCP4.5 or FCP4 installer DVD.
2. Copy the invisible "Installer" folder to the hard drive.
3. Navigate into the "Packages" folder inside of this folder on your hard drive.
4. Open each package (LiveType.pkg, FinalCutPro.mpkg, etc.) and delete the file "InstallationCheck" inside of the Contents > Resources folders for each .pkg or .mpkg
5. Install as usual with the FinalCutPro4.mpkg from the folder copied to the hard drive.
Installation should proceed as normal. One more step is required to get it to run, though.
After installation and before launching any of the programs, open each application package (Final Cut Pro, Compressor, Soundtrack, etc.) that was installed inside the Applications folder, and edit the Info.plist file inside of the Contents folder of the application with TextEdit or your favorite plain-text editor. Simply delete the lines and tags that would prevent running on your machine. For example, to get it to run on a G3/300, you would delete the following lines, or simply change them to match your system:
<key>AELRequiredCPUType</key>
<string>G4</string>
<key>AELMinimumCPUSpeedSingle</key>
<string>350</string>
...as well as the "AGP" key and value, but I don't know the exact line since I'm running it on a G4 PCI machine and have deleted that line already.
Voila! A working FCP installation with all the helper apps.
One last word: to install updates to FCP or any associated application via Software Update, simply tell Software Update to download the updates only without installing. Then, repeat the procedures outlined above for the updater packages (deleting the "InstallationCheck" files from within the package). After you install the updates, you may need to edit the actual application's Info.plist file again, as the updaters will restore the deleted lines to their default values of requiring a G4 and AGP slot.
I've been doing this since FCP4 came out to get it to run on various G3s and upgraded G3s. Flawless every time. Yes, we have FCP licenses for each machine, and I don't think editing those files would constitute illegal activity.
This procedure should also work for any other application that refuses to install on your machine because it doesn't meet the installation requirements or won't run because of some pesky Info.plist entries.