Please bare with me as I rant in real time as I'm on hold with the Origin support guy. I can't imagine being that guy. I used to do tech support. It was one thing doing it via phone. It's another doing it via real-time chat. I've sent him a few screenshots to show him what I've been seeing.
Edit: to the Origin support guy who is probably desperately doing Google searches for the issue. Hello. Welcome to FBG's. It's not your fault that Origin sucks.
Just finally got a response from the esculation guy on the issue (yes, it took them over a week to get back to me). Origin does not have an option to put my remaining wallet balance toward ($45.11) toward Battlefield 4 Premium membership ($49.99). The balance must be higher than the cost. I've never had the issue with Steam. In fact, I can't think of any retailer in America where you cannot use a gift card and still use a separate payment type to pay off the remaining balance. With the exception of Origin, that is. What a ####### joke.
So basically, I'm going to have to buy another $20 card to get my balance high enough to cover Premium. I guess what I'll do is buy Mass Effect 3 with the remaining balance during a $10 sale. I've always put off buying it because of Origin. But now Origin has my money held hostage and I don't really have an option.