I just now figured out how to get the data off the game disc and avoided downloading 23 of 28GB. So I only need to download 5GB of data, which would be the patch updates and the free DLC. The solution is pretty simple. You only need to do this if the installer on the game disc is not working.
1) Copy these 4 files off of the relevant DVD discs, place all of them in the same location (Place them all on the desktop for example). If I made a mistake in regards to which file is on what disc, don't worry, the gist of what I want you to do during this step should be obvious.
Disc 1: DA3Game.z01
Disc 2: DA3Game.z02
Disc 3: DA3Game.z03
Disc 4: DA3Game.zip
2) Open EA Origin software.
3) Register your product key and begin downloading Dragon Age: Inquisition.
4) Pause the download after 10~ seconds and then quit EA Origin.
5) Locate where the game is being downloaded/installed to.
6) Open any of the 4 files I told you to copy off of the game discs in Step 1, use WinRAR 5.30 for opening the file (Don't use 7zip).
7) Extract the contents to the same location that the game is being downloaded/installed to (location identified in Step #5). Note: You only need to extract the contents of ONE of the 4 files, the contents of the other files will be automatically extracted during the operation. Overwrite any files that already exist in the destination folder.
8a) Open EA Origin software and resume the game download. EA Origin will verify the integrity of the existing files (the files you extracted) before resuming the download.
8b) Watch as it jumps to 23.xx GB downloaded once it finishes verifying the files on the HDD! (It will say "Resuming download" during the verification process, once it finishes and the download actually begins it will change to say "Downloading")
9) Done.
Note: You might think something similar can be done for Steam games that suffer a similar issue, you're assumption is wrong. Steam games use encryption which prevents you from extracting the game content from the installation files.
Edit: DLC will always need to be downloaded and will be downloaded after the main game has finished updating (Main game is 28~GB).