You're doing really good work. The shelter environment is hard on dogs, and it sounds like your routine is helping this guy.
My guess is that he never really has a chance to decompress. His shelter environment is better with the enrichment, but still stressful. He's worked up on the walk. Country/forest walks are excellent for decompressing under normal circumstances, because they let a dog sniff and 'be a dog' in nature for a while, but as you're noticing, it's not really enough to overcome all the other environment stress he's dealing with. It can take a few days for stress hormones to flush from a dog's system, and he may just not really be getting the chance to unwind. But it definitely sounds like it's better than before this program started!
My poodle is easily overstimulated, especially on walks when other dogs show up. One of the things that helps (aside from keeping as much distance as possible), is sniffing games. Either a treat scatter so he has to break focus on the other dog to hunt down goodies, or a game where we toss one treat to the left, as soon as he finishes and looks up we toss another to the right, repeat until he seems more settled. If he's too worked up to pay attention to the treats, we're typically too close to the other dog and just need to get more distance before trying again. With many dogs, if they're too worked up to eat they're too worked up to learn (assuming they're enthusiastic about treats under normal circumstances).
I disagree about the muzzle. If you think there's any chance he might put teeth on another dog despite your best efforts (you can't always control when someone's going to let their loose dog run up to you, of course, and dropped leashes/equipment failures happen), a muzzle is a great choice. So long as you use a basket style that he can drink and pant in (and ideally take treats through), and you introduce it positively to him so he's comfortable about wearing it. The Muzzle Up! Project has a website with lots of great resources about how to train this and why muzzles are excellent tools for every dog to learn how to wear. If it makes you more confident about handling him in public and prevents him from getting a bite record, it's absolutely worth it.
My guess is that he never really has a chance to decompress. His shelter environment is better with the enrichment, but still stressful. He's worked up on the walk. Country/forest walks are excellent for decompressing under normal circumstances, because they let a dog sniff and 'be a dog' in nature for a while, but as you're noticing, it's not really enough to overcome all the other environment stress he's dealing with. It can take a few days for stress hormones to flush from a dog's system, and he may just not really be getting the chance to unwind. But it definitely sounds like it's better than before this program started!
My poodle is easily overstimulated, especially on walks when other dogs show up. One of the things that helps (aside from keeping as much distance as possible), is sniffing games. Either a treat scatter so he has to break focus on the other dog to hunt down goodies, or a game where we toss one treat to the left, as soon as he finishes and looks up we toss another to the right, repeat until he seems more settled. If he's too worked up to pay attention to the treats, we're typically too close to the other dog and just need to get more distance before trying again. With many dogs, if they're too worked up to eat they're too worked up to learn (assuming they're enthusiastic about treats under normal circumstances).
I disagree about the muzzle. If you think there's any chance he might put teeth on another dog despite your best efforts (you can't always control when someone's going to let their loose dog run up to you, of course, and dropped leashes/equipment failures happen), a muzzle is a great choice. So long as you use a basket style that he can drink and pant in (and ideally take treats through), and you introduce it positively to him so he's comfortable about wearing it. The Muzzle Up! Project has a website with lots of great resources about how to train this and why muzzles are excellent tools for every dog to learn how to wear. If it makes you more confident about handling him in public and prevents him from getting a bite record, it's absolutely worth it.