No download button in Origin

I'm writing this here because I refuse to queue in the chat line for another 15 minutes just so I can be glad-handed away by one more underpaid intern, and EA apparently has no email contact option.

My name is James. My Salesforce/EA Help case number is #37508438. My Origin Error Report ID is 0d30749d90001b2d . I have been trying to download Mass Effect Andromeda (which I received for Christmas) for several hours, and I have spent the past hour on support with EA techs.

The problem is really very simple: when I open Origin, it refuses to give me the option to download or play Mass Effect Andromeda (I can play my other games as normal). There is simply no button there. (See attached image.) At the direction of EA techs, I have restarted Origin, reinstalled Origin, wiped Origin's cache, and run Origin as an administrator, all without effect. I have relayed my redemption code to EA "Game Advisors," who appeared to verify its validity.

In my last support contact (attached PDF), the tech asserted that my files are corrupt and promised to email me "advanced steps" which "will work for sure"... just as soon as I closed the chat with her. Needless to say, no "advanced steps" ever arrived. (I've waited a full hour, just to be sure.) So here we are. Unfortunately, since this game was given to me as a Christmas present, it appears to fall outside EA's refund policy, so I can't just abandon ship and spend the money on a real platform to get PUBG or some such.

This technical nonsense with my old enemy Origin is exactly the reason I held off on buying Andromeda for the better part of a year, and now I'm kicking myself for having given in just because I love this franchise. So, questions:

1) Can anyone -- from EA or elsewhere -- help me resolve this? At first, I thought I must be overlooking something obvious, but after getting the confused brush-off from two techs, I'm starting to think this issue is something weird and confusing.

2) At this point, after investing hours trying to turn on a game I might very well not even play for very long, is there any morally or legally compelling reason why I shouldn't simply pirate the game -- which, remember, I've already paid for -- and then never purchase an EA product again?

EDIT: Oh, and, for completeness' sake, I've attached my DxDiag.