Some beardie babies don't thrive well, when they've not been well cared for from the beginning. So when they're sick like your little one is, it takes awhile before they get better. You're doing all the right things, the Pedialyte is great to give him by syringe. You can also put it into his baths, it will help him, too.
The babyfood I've always gotten is organic butternut squash & chicken, but it would be better that he not get a lot of protein right now, it could be too much for his little body.
Do you have a reptile vet in your area? That would be where you could get Carnivore care & that would be a good thing to mix in with the veggie baby food. Just a tsp of it & a pinch of calcium daily 5 days a week, then vit/min powder, again just a pinch, 2 days a week. Mix it all up and drop it on his nose by syringe so he'll lick it up. That's what I've always done with sick beardies and it's worked for those that are strong enough to live. I'm so hoping your little one gets stronger. You can feed him the pedialyte 1:1 a few times a day, too.
Any other questions you have, just ask. What are the ingredients of the Nat Geo food? Let me know, as it might be good for him in small quantities.
I'm not sure why he has the runs, he might just not be digesting very well. So check into a reptile vet in your area, you might need to take him in for a check up & fecal test.