I initially had this issue, which infuriates me! I hate Origin but i need these games in my life :D
I have Origin installed on one of my external hardrives, buti dont see it changing anything.
I renamed Origin to "Old Origin" (or whatever you like) and deleted my current copy of Origin using it's standard uninstall.exe, which kept my other games folders untouched.
I reinstalled Origin straight from the Dragon Age (disc1) Inquisition setup.exe.
Once Origin was updated and Installed again i logged in and instantly began installing Da3 conventially, with no mention of downloading a single thing.
Obviously on "old Origin" i had redeemed the code in my retail case, so the new origin already had it on my profile once i logged in.
