Tell Spike that I'm a Corona and lime drinker too! He has good taste!
I use a harness and leash for all 3 of my dragons, not that you can "walk" them, well not my dragons anyway, but I have always thought that the harness and leash is necessary if you're going to have them outside and not in a cage or tank, because if they take off you're not going to catch them! They move like bullets, it's incredible how fast they run.
I have actually taken my large female with me while walking my dog, I have her on her harness and her leash is around my wrist (it has a clip on the end so I can wrap it around my wrist and then secure it), and she is typically in my front hoodie pouch with her head sticking out the entire time. She loves it, she looks at everyone and everything going by, cars and other dogs, birds, etc. She seems very confident and secure when she's in my hoodie pouch or I'm holding her in my hands, as opposed to if she's on the ground and a bird flies by, she'll take off like Lolo Jones when that happens, and then she tanks herself at the end of the leash ?. But the harness and leash is ALWAYS ON HER if she's outside, period. Just like my parrots, they all have Aviator Harnesses so they can go on walks, hikes, to stores, etc. They'll be on my shoulder and their leads are also around my wrist, they typically don't jump off my shoulder and their wings are clipped, but birds that are clipped have been known to catch wind and actually fly for miles. So I'm always 100% safe with all pets out of the house. My female beardie actually rides in the carts at stores, she's on the harness and leash, which is around my wrist, and then she sits in the child seat in the top of the shopping carts that folds down. She loves it, she bounces back and forth, side to side, hanging over the edge of the cart and looking at everything.
I just use one of those adjustable lizards harnesses that has the piece that their two front legs go through and then it cinches around their chest and has a 4 foot lead with a clip on it attached to the harness. I think I paid $10 a piece for them at Petco, I think Amazon has them for a few dollars less. Honestly I wasn't sure if they would hold up, it's just a really thick, stiff piece of leather/suede with a cinching mechanism and a 4 foot nylon lead. But I've been using my oldest girl's for almost a year now, I use it quite a bit too (usually she goes with me whenever I go to Petco, Home Depot, or Lowes), and it's still like new. And she has never messed with it at all, it must not bother her because she hasn't touched it since the first time I put it on her at about 3 months old. It works so well and has held up so well that I bought the same one in a different color for my newer 3 month old baby boy a few weeks ago, and he went a little spastic the first time I put it on him, but after about 5 minutes he calmed right down and now he's fine with it. He's still too small for me to feel comfortable with him out all over the place or in the car, he doesn't yet sit still, lol. But he'll be using the same harness and leash soon.
They also make beardie "hip harnesses", which are the same principle but they go around their back legs. I've never used one of those so I can't give any info about them, good or bad. I have seen other people with photos of their beardies wearing them though.
As far as taking your beardie on an actual hike in a National Park, I think he'd love it if you can figure out how to take him along comfortably and conveniently. If he sits still and your hikes won't be too intense or physical you could put him on a harness and leash and do the hoodie pouch thing, but you definitely don't want to put him on your shoulder, I've seen people doing that outside on walks in the woods and on hiking trails, some even without a harness, which is really irresponsible and stupid.
As far as using a backpack, if you're willing to spend some dough they make these absolutely wonderful backpacks for pet birds where the bird stays in a special screened-in compartment where the actual "pack" part usually is. So they look and function like a normal backpack, but it's like they have a built-in cage for your bird to sit in that they can fully see everything out of, and they come with a removable perch and stainless steel bowl, and also do have several small storage compartments for you to put stuff in. They come in different models, sizes, and colors (a size small or extra small would work for a beardie, and you obviously don't need the fancier models with perches).
I have a size medium that I bought used on eBay for my Senegal Parrot, Kane, and he loves going in it to bits. It's a little weird with a parrot in one because he's on my back, I can't see him at all but he can see everything and people can see him, so people are constantly coming up behind me and talking to Kane, not to me, lol. But I can't tell the difference, so I respond and realize that they are talking to my bird. He also is a little smart-ass Senegal Parrot which doesn't help, he'll get tired and start spitting his pellets or veggies out of the bowl he has in there, and he'll start yelling things out in the middle of Home Depot like "Give me kisses!" and "You're my baby!", and I know people who are in front of me and can't see that there's a parrot on my back think I have Tourettes Syndrome or something...?
The expensive backpacks like this are made by Celltei, and are called "Pak-O-Bird", and are ungodly expensive new, like $150 for a small one, I got my orange medium one on eBay slightly used for $90, which was a steal... However, A&E Cage Company (very respected bird supply company) makes a very similar backpack, not quite as fancy as far as little compartments and they have a removable perch but not a bowl, which you don't need either for a beardie of course, and I think the small costs $36 new on Drs. Foster and Smith, and if you go on Amazon or EBay you'll see both of these brands new and used for different prices. I was just going to buy one of the cheaper A&E ones at first, but I do a lot of mountain biking, camping, hiking, and urban exploration, and the Celltei brand backpacks are very rugged and versatile, they look like an Osprey or Kelty type of backup with an animal cage built in, they're great and will no doubt last forever.
The other option is making your own custom backpack with a built-in beardie cage in the back that allows your beardie to see out both sides and the front. I found a plan for making one (before I bought the Celltei Pak-O-Bird I was going to do this project) on Indestructibles.com that was for birds and involved actually attaching a small bird cage to the back of the backpack. However, I was actually thinking about making a custom one for my beardies, it's actually really easy to make one just like the really nice Celltei ones if you're a little handy and have basic tools. I think I'm going to attempt it, I'm going to buy one of those cheaper hiking backpacks at Walmart, like an Ozark Trail or Outdoor Products brand one (these are cheap but actually really, very nice, especially for the prices) so if I mess it up I'm not destroying my $300 Kelty hiking pack or an expensive daypack, I have a couple Burton Skateboard and Snowboard backpacks that I love). Both Ozark Trail and Outdoor Products make hiking backpacks with removable aluminum internal frames, which gives the back of the cage compartment support, and the cage compartment something rigid to attach to. So if I actually try this and it turns out well I'll definitely post photos with instructions.
Bottom line, I think it's a great idea to buy a harness and leash for your beardie, it's a must if you're taking him outside and is definitely something I'd buy before taking him on a cross-country road trip in a vehicle. It will be incredibly easy to just keep him on the harness and leash while in the car during the entire trip (they don't mind them at all) so he can bounce all over the car, looking out the windows and sitting up on the dashboard, then when you go to a rest stop you can just grab him and put him out in the grass for some exercise and natural sunlight. I also think taking him on hikes in national parks is a great idea, but only if you have a secure backpack with a cage compartment that he can see out of, get proper air flow in, and move around in. I think beardies really would enjoy being in a backpack in the forest or in the mountains, seeing and hearing all the outdoor sights and sounds. Do some research and you'll find many pet bird backpacks that you can easily modify for your beardie, really by only removing the perch.