Thank you for the responses! To clarify some things -
We all live together - I moved in to their house almost ten years ago, after dating my partner ("Husband") for about a year. Wife and I are not romantically or sexually involved. Mostly because I'm 90% gay, but also I think the two of us just don't "click" on a number of levels.
I know it isn't my responsibility to fix their relationship, and Husband certainly hasn't told me to fix it, but he seems stuck and out of ideas, and I want to help. This is a research/brainstorming thing, not some kind of blame-the-secondary thing. Even if I was just his good friend and co-worker I would want to help, because I can see he's been struggling with this for over a year, and hasn't made any real progress. In any case, I don't think you can last ten years as a happy secondary without figuring out that if the primaries are unhappy, that is bad news for everyone, and being helpful in attempting to find a resolution is in your best interest.
Sagency - Those are some really great ideas. I'll talk to Husband about them. It hadn't occurred to me that Wife might like to know about all the times when Husband deprioritizes Boyfriend (me) in order to do things for her. I think that on some level he's always assumed she'd feel awkward knowing that her special whatever happened at my expense. That it would contribute to a "scarcity mentality" and promote the idea that she and I were in competition for his time and attention. But... if it is a "competition" that she almost always wins... maybe she'd like that?
I was especially struck by your last point about encouraging Wife to have more things outside the house and the relationship. Now that I think of it, the problem became most obvious soon after she retired from her job, and she's just not the "stay at home housewife" type. I wonder if it isn't so much that she resents when Husband's job takes him away from her, but that she is jealous because she wishes she had a fullfilling "important" career like his that got her attention and praise from other people. Which might explain why attention and praise from him seems like it is "never enough".
SNeacail - I'll check out 5 Love Languages - Thank you! As a third-party observer, it does seem like they've got very different ways of showing their love for each other. That could be another piece of why his praise/attention is "never enough". It seems like even his best attempts to show her how special she is keep missing the mark, and he isn't able to figure out why. It makes sense that he might be aiming at the wrong place.