It does sound like there are many issues here, long-term issues about the relationship between you and you wife, and individual problems as well. I'm not surprised this is not easy to resolve or handle. I would second the suggestions regarding therapy; if you cannot afford it together, maybe individually? For example, you don't mention what's behind the lack of intimacy (or desire) that naturally bothers you on your wife's side, it sounds like perhaps working though it with some professional help might have some benefits.
You are saying that you prefer to express yourself with your actions rather than words, but then you also say that you have distanced yourself from your wife for a good while, and you two obviously have communication problems. Have you tried to have open, honest conversations with her where you would start saying you would really like to understand what's going on on both sides and find out what should be done differently to improve the relationship? Do you know what the sources of her insecurities are? You seem to be frustrated that your "years of action" does not have result as far as the relationship goes, but probably most of your actions have been targeted towards yourself, to straighten out your own life. Not the interface between you two.
I'm also the kind of person who thinks actions speak louder than any words could, but sometimes saying the right words, words that the other person likes to hear, can work wonders. It really is just a form of doing things to each-other that the other likes sometimes, even if it's not our most natural course of behavior. Not lies, but adding a few kind words... how can those hurt? Maybe just think about the support here on SR. People clearly have many different styles of expression and supporting others, and also what type of support they find most helpful.
As for amends, if you want to apologize for the past, I would not come up with it out of the blue, but would probably try to embed it in an open and honest conversation I suggested above. If your wife tends to have guarded, angry responses... have you considered writing a letter to her expressing your feelings and apologies? I once had a boyfriend who had tons of personal insecurities coming from far past issues and lots of others, and he had a real hard time with serious f2f conversations. But we could "talk" about anything in writing. Did that for a while, and eventually speaking had become easier as well.
The amends in my mind don't necessarily need to be actions targeting or relating to the past. Could be any kind of support regarding to present problems, something she is struggling with, things where you could help here and now. I would probably choose things (at least initially) that are absolutely not suggestive of your desiring anything in return, expecting intimacy, etc. More neutral, practical things.
I was in a ~3 year-long relationship at the time when I quit drinking that underwent some pretty intense changes in dynamic when I got sober and started doing things differently. Eventually we decided to end it, but that decision was preceded by many many long and honest discussions, the communication was very good. But of course I did a lot of bad things while I was drinking, not abusive, but I really distanced myself from my partner emotionally, did not keep promises, was lying, etc. So when I sobered up, we talked about these past things also a lot. We are still colleagues after breaking up, so what I try to do is help her with work-related things and other practical things when there is a chance, she appreciates it.
I think it's possible that your wife might not accept your amends or would have problems expressing any appreciation as it seems she carries many resentments right now. This is where it would be important to do it in a way that makes it as clear as possible you are not performing these acts in anticipation of any sort of reward.
I would not expect the relationship to be fixed simply by making amends though, in my mind it would just be a necessary step and lot more work would be required.