Wow, you guys have both been through a LOT!
First of all, it sounds like you both have done a tremendous amount of work to help get him as healthy and functional as possible. Kudos for that.
Secondly, I really think he needs to be evaluated by a clinical neuropsychologist to help define what is stroke related, what is depression related, and what tools might help him overcome these barriers. Even though he fell back on his head, he probably has affected other parts of his brain (especially the frontal lobe) which can cause significant issues because that part of our brain is so critically important. It could be that he's had some brain injury from the strokes and the falls, that together have affected his ability to have a can-do attitude, to initiate tasks, to not get distracted, to feel more positive, to have better control over irritability, and other things that you fear he's doing on purpose. You can also then get recommendations to take to a psychiatrist to see what medications might help him function better cognitively and emotionally.
Lastly, have you had time to work through your own psychological baggage? Having your husband go through so much, and be lucky to be alive, while probably still having a fear in the back of your mind that he could have another stroke or die at any time, is a LOT to juggle emotionally, You may need some counseling in order to have a safe place to process all the past stuff, and the current fears, anxieties
, worries you have. You also need to make sure that you're still taking care of yourself, and not devoting so much time and energy to his care that you're leading yourself to emotional burnout.
But overall, I hear you describe symptoms we would expect to see in people with brain injuries, so it's not all within his control. I don't think he's being lazy. I just don't think he's been evaluated completely and given the proper tools to help deal with the cognitive and emotional aspects of his injuries.