Thanks for your kind words. PS Jimmy Button is a childhood hero of mine back when I was racing motocross every weekend. Dude ended up breaking his neck and being diagnosed a quadriplegic but walked 2 years later. Sorry for the diversion, your handle reminded me of that...
Anyway, your brother's situation warrants some heart to heart (or maybe a come to Jesus) talk about what he really wants out of life. I can't tell you how many times I've counseled friends/family/ex clients on what they should be doing diet-wise in order to reach their goals and then, at some point, I hear the complaint I'm not losing weight and I'm doing what you said! At first, this really upset me and I thought man, I need to tweak their intake or give them better instructions. So, I'd dig and dig, scouring research and innovative tricks to get people to comply. Sent annotated emails rife with cited literature and personal guidelines and still, nothing happened. Then I realized something, 9/10 times they just weren't doing what I wanted them to do at even an B level. One lady told me she was "pure paleo" but ended up putting down 2-3 jars of almond butter in a week + gluten free treats. A guy tried to reason with me that he thought the chicken wings served at the bar was the best option because, after all, they ARE chicken.
At any rate, I finally figured out that 9/10 of the people who don't get results from changing their dietary habits simply aren't following the protocol. This may be reflective of a protocol that's inappropriate for their current level of commitment or lifestyle or it may just be a knowledge gap for how the darn thing actually should be followed. I will admit, however, about 1/10 of these cases presents with someone who is rigidly following a good plan but has buggered there metabolism so much by starvation, too many competitions without an off season, etc. and these folks require some serious leg work on their coach's end to get them back to where they need to be.
In my opinion, it is highly likely that your brother's version of Paleo is not appropriate for what he needs right now. If it were me setting it up for him, it would be chock full of lean protein sources, fiber-rich vegetables, 1-2 servings of fruit per day, and a limited amount of added fats in the way of cooking oil, salad dressings, etc. I don't believe that having a super big cheat meal 1x a week would do anything positive for him, but perhaps you could get some better initial buy in with him if you advised him on my previous recommendations with the incentive of the following:
1x per week you get to go wild with a few stipulations: 1) This meal has to be eaten away from the home, i.e. go out to eat. 2) You cannot eat this meal solo, but rather you have to be with friends, family, etc. 3) You have 1 hour to eat, from 1st to last bite. and 4) You can't take home any leftovers.
You're also correct on the HIIT recommendation. I'd stick to the rower for him at a 2-3x /week frequency at this point since he's clearly not interested in strength training and the guy needs to do something hard to help his metabolism and drive an adaptation. I'd stick to the rower as well because it'll be a better modality for him to really push the intensity hard versus having to learn a higher skill motor pattern like KB swings or similar.
Finally, I believe preparation is the name of the game in this situation. Making double servings of lean proteins each time he cooks, i.e. if he's eating chicken make two or if he's making eggs, make double for later. A whey protein supplement might be a good option too so he's never "stranded" without good choices. Finally, he'd likely get some benefit out of r-ALA and chromium picolonate supplementation. Hope this helped.