Hi Blackrook What you are doing is great but it seems to me you are caught in a mass of guilt. Everybody makes mistakes and some of them are pretty bad, but that is life. You have to learn from them and move on. An ideal marriage is not based on one partner trying desperately to atone for whatever he did to upset his W.
I'm not saying you shouldn't do things to try to please her. But the point is you don't have to prove you love her, you just have to act in a normal loving manner towards her all the time from now on. If you tell her you love her and she doesn't believe it, this says more about her than about the way you are acting.
Yes you treated her badly, but you were depressed and not your normal self. So give yourself a break. At the same time you say "how dare she not know that I love her". Again I think this anger towards her comes from guilt. You know that the way you treated her caused her to feel this way and you feel bad about that. But again give yourself a break. You did not set out to maliciously cause her pain. In fact this was probably a side effect of your own pain. If you can forgive yourself for your mistakes you will be able to feel sympathy for her and treat her with the love she needs to heal.
To make things right you need to be in a positive frame of mind. This is a new era for you, so forget about what is past except in terms of not making the same mistakes again. Treat your wife as you would treat someone who had been hurt before in a difficult relationship. Be kind and reassuring, give her time and space if she needs it. Let her see that you are trustworthy. Be the kind of guy she fell in love with again, and regard the recent problems as a blip. Its OK to apologise for what you did, as long as you remember that was in the past and you are better now. Life is too short for regrets.