Thanks, all, for the tips! I guess I'll go ahead and confirm "origin digital deluxe"--even though that's not exactly what I have--since that's the only option they're giving me when I input my key. Just hope I'll be able to install from my discs since I certainly don't want to download the game. It seems like it wouldn't be too much effort for EA to offer different confirmation screens for deluxe and digital deluxe--and that "follow the on-screen instructions" is pretty thin as installation guides go, especially, when on-screen instructions are lacking, but I guess EA is determined to confirm my impressions of them.
I think you should still be able to use the disks - in this respect, the physical deluxe is identical to the digital deluxe, and you're just unlocking the game to your Origin library, to download whenever.
I got a boxed edition of Skyrim way back when (it was actually the game that got me onto Steam - outside of Blizzard, I hadn't been a PC gamer for over a decade) and I was able to install it using the disks, but the key obviously unlocked it on Steam, for me to download again whenever I wanted to.